CHARTOGRAPHY 


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CHARTOGRAPHY 

IN  TEN  LESSONS 


BY 

FRANK  J.  WARNE 

AUTHOB    OP 

warne's  book  of  charts 

warne's  elementary  course  in 

chartography,  etc. 


ILLUSTRATIONS  BY  H.  F.  CHURCH 


PUBUMUEI)    DY 

FRANK  J.  WAHNK, 

SOUTHDMN    HUM, DING 

WASHINGTON.  D.  C. 


q^G 


Copyright,  1919,  By  F.  J.  WARNE 


(Authorship  also  protected  in  Great  Britain  and 
her  Colonies,  including  Canada) 


TABLE  OF  CONTENTS 

Page 

Preface vii 

Introduction Ut 

Lesson   I 

Building  the  Chart 

Value  of  Table  of  Contents 1 

Statistics  and  Chartography 3 

Definition  of  a  Chart        3 

The  Statistics 4 

Horizontal  Lines 5 

Vertical  Lines " 

A  Choice  of  Methods 8 

The  Use  of  Pencil  Dots 10 

The  Framework 10 

Lesson  II 

The  Scales 

Statistical  Variables       13 

The  Independent  Variable 13 

The  Dependent  Variable      14 

The  Horizontal  Scale         15 

Determining  the  Vertical  Scale 15 

The  Scale  Lines 16 

Reading  the  Scales 1 ' 

Plotting  the  Statistics       19 

The  Use  of  Cradicnlcs       20 

iii 


iv  Chartography  in  Ten  Lessons 

Lesson  III 

The  Curve  Chart 

Page 

Making  the  Curve  Heavier      25 

The  Horizontal  Scale  Unit       26 

Squares  Should  be  Equal 27 

Effects  of  Different  Scale  Units 28 

Dropping  the  Zero  Line 30 

Indicating  the  Absence  of  the  Zero  Line 31 

Divisors  for  the  Vertical  Scale 33 

Lesson  IV 

Features  of  a  Complete  Chart 

The  Statistical  Table 37 

Table  Should  Appear  on  Chart       39 

The  Make-Up  of  the  Table 40 

Spacing  the  Columns 41 

The  Form  of  the  Table 42 

Duplicating  the  Scale  Units 44 

The  Place  for  the  Horizontal  Scale 44 

Word  Designation  of  the  Scale 46 

The  Title 47 

The  Foot-Notes 48 

The  Neat  Lines      49 

Lesson  V 

The  Bar  Chart 

Making  Bars  from  a  Curve 53 

Making  a  Curve  from  Bars 55 

Advantages  of  the  Horizontal  Bar 56 

Reversing  the  Scales 57 

Width  of  the  Bar       59 


Table  of  Contents  v 

Page 

Separation  of  the  Bars 60 

Location  of  the  Table 61 

The  Bar  and  the  Curve 62 

Lesson  VI 

The  Tools  of  the  Chartographer 

Cross  Section  Paper      65 

The  Lead  Pencil 69 

The  Kind  of  Ink 70 

The  Ruling  Pen 71 

Correct  Position  for  Holding  Pen 71 

Pen  Points 73 

The  Drawing  Board      74 

The  T-Square 75 

The  Triangle 75 

The  Engineer's  Scale 77 

The  Dividers      78 

The  Essential  Tools 79 

Lesson  VII 

Accuracy  in  Chartography 

The  Use  of  the  Typewriter 81 

Drawing  Letters  for  the  Title 83 

Exaggerating  the  Curve 86 

Effects  of  Exaggerating  the  Curve 88 

Advantages  of  Extra  Squares      91 

Lesson  VIII 

Curve  and  Bar  Designations 

Disadvantages  of  the  Unbroken  Curve 93 

Curve  Designations       95 


vi  Chartography  in  Ten  Lessons 

Paob 

Word  Designations  of  Curves 98 

The  Peak-Top  Curve 99 

Determining  the  Scale  Spacing 101 

Utility  of  the  Curve  Chart 102 

Chartography  Based  on  Comparisons 103 

Bar  Designations 105 

Interpreting  the  Bar 108 

Some  Characteristics  of  a  Good  Bar  Chart       ....  109 

Word  Designation  of  Scale  Units Ill 

Lesson  IX 
Value  of  Statistics  to  Chartography 

The  Statistical  Table        II4 

Aids  in  Reading  the  Table       Il6 

The  Substitution  of  Ciphers        II9 

The  Table  of  Ratios      120 

Building  up  a  Table      12l 

The  Percentage  Increase  and  Decrease 123 

The  Zero  Line 126 

The  Arithmetic  Average 129 

The  Misuse  of  the  Average 13l 

Statistical  Class  Limits 132 

Lesson  X 
Primary  Principles  of  Chartography 

Planning  the  Chart 137 

Importance  of  the  Right  Method 139 

Essentials  of  Good  Chart  Making      140 

Planning  the  Size  of  the  Chart 141 

Planning  a  Reduction  in  Size      143 

The  Reducing  Glass      147 

The  French  Curves 149 

Checking  up  the  Completed  Chart 151 


PREFACE 

No  attempt  is  made  in  these  ten  Lessons  to 
cover  the  entire  field  of  chartography.  To  do  so 
adequately  would  require  several  large  volumes. 
All  that  these  Lessons  aim  to  do  is  to  familiarize 
the  student  with  the  primary  or  elementary  prin- 
ciples. These  underlie  chart  plotting  and  con- 
struction as  applied  to  the  curve  and  bar  charts. 
These  principles  are  applicable  to  all  kinds  of 
charts,  variations  being  explained  by  the  differ- 
ences in  the  circumstances  surrounding  the  special 
j)roblems. 

These  Lessons  are  the  by-product  of  an  experi- 
ence covering  a  period  of  ten  years  during  which 
time  the  author  has  been  engaged  professionally  in 
the  application  of  the  principles  of  chartography 
to  the  working  out  of  practical  problems  of  the 
work-a-day  world.  In  the  presentation  by  means 
of  diagrajns  or  charts  of  innumerable  statistical 
problems  the  author  has  been  able  to  put  the  art 
of  chartograi)hy  to  a  severe  test  before  such 
authoritative  tribunals  as  the  Interstate  Com- 
merce Commission,  various  state  public  utilities 
and  railroad  commissions,  boards  of  arbitration 
af)f)oirit('d  by  the  President  of  the  United  States 
for    the   peaceable   .settlement   of   labor   contro- 


viii         ChartograpUy  in  Ten  Lessons 

versies  and  various  committees  of  Congress.  In 
this  professional  work  he  has  been  called  upon 
to  till  entirely  new  fields,  for  there  were  few 
authoritative  guides  to  follow,  and  in  conse- 
quence he  has  been  compelled  to  pioneer  his 
way  amid  innumerable  uncharted  difficulties. 
Such  an  experience  should  contain  lessons  of 
value  to  others  engaged  an4  about  to  engage  in 
the  making  of  charts.  In  presenting  this  formu- 
lation of  the  principles  of  chartography  the 
author  begs  leave  to  express  the  hope  that  these 
Lessons  may  serve  the  beginner  in  chartography 
as  a  safe  guide  over  the  innumerable  pitfalls  that 
inevitably  must  be  encountered  unless  he  is 
warned  to  guard  himself  against  them. 

An  endeavor  has  been  made  to  bring  these 
Lessons  within  a  reasonable  price  to  the  student. 
The  cost  of  production  of  "Warne's  Elementary 
Course  in  Chartography,"  which  was  published 
two  years  ago  and  the  price  of  which  was  fifty 
dollars  for  the  twenty  Lessons  (including 
"Warne's  Book  of  Charts"),  was  such  as  to  pro- 
hibit a  lower  price,  and  in  consequence  it  could  not 
be  made  to  serve  the  class  of  students  the  author 
desired  most  to  reach.  Parts  of  that  Course  have 
been  completely  revised  in  these  Lessons. 


INTRODUCTION 

The  Value  of  Chartography 

(Revised  from    "Wame's   Elementary   Course   in 
Chartography"  and  "Warners  Book  of  Charts.") 

To  the  average  citizen  statistics  are  as  incom- 
prehensible as  a  Chinese  puzzle.  To  him  they 
are  a  mental  "Mystic  Moorish  Maze."  He 
looks  upon  columns  of  figures  with  suspicion 
because  he  cannot  understand  them.  Perhaps  he 
has  so  often  been  misled  by  the  wrong  use  of 
statistics  or  by  the  use  of  incorrect  statistics 
that  he  has  become  sceptical  of  them  as  repre- 
senting reliable  evidence  as  to  facts  and,  like  an 
automaton,  he  mechanically  repeats  "while 
figures  may  not  lie,  all  liars,  figure,"  or  the 
equally  common  libel,  "there  are  three  kinds  of 
lies — lies,  damn  lies  and  statistics." 

And  yet  statistics  are  an  infallible  indicator  of 
economic  conditions — they  measure  the  heart- 
throbs of  a  nation's  or  of  an  industry's  life- 
blood.  They  register  the  conditions  of  any  given 
static  situation;  they  point  the  direction  of  a 
trend  or  tendency  with  the  accuracy  of  the  ther- 
mometer in  measuring  the  temi)crature. 
!(-,'»; Every  business,  wliether  organized  on  a  large 
or  a  small  scale  needs  statistics — in  fact,  statistics 


X  Chartography  in  Ten  Lessons 

are  vital  to  its  successful  existence.  Without 
them  the  executives  cannot  know  the  status  or 
tendency  of  the  economic  factors  which  control 
their  affairs.  This  practical  value  of  statistics 
in  every-day  business  life  is  coming  to  be  more 
and  more  correctly  appraised  at  its  true  worth. 
The  Railway  Age  of  February  23,  1917,  says: 

An  officer  of  a  western  road  recently  made 
the  statement  that  each  department  of  a  large 
railroad  system  should  have  on  its  staff  a  thor- 
oughly competent  man  whose  duty  it  should  be 
to  analyze  statistics.  The  assertion  was  not 
made  without  deliberation,  and  it  might  be  perti- 
nent to  ask  whether  we  are  getting  the  most  out 
of  the  statistical  department.  The  amounts 
which  are  spent  by  American  railroads  in  com- 
piling statistics  bearing  on  the  functions  of  the 
various  departments  are  extremely  large,  and  no 
one  who  knows  the  importance  of  the  compara- 
tive figures  to  the  officers  will  question  the  wisdom 
of  the  expenditure.  Some  of  the  statistical  data 
which  the  railroads  compile  is  readily  analyzed, 
and  the  important  figures,  such  as  average  tons 
per  train,  or  pounds  of  coal  per  thousand  gross 
ton-miles,  are  always  readily  available.  A  closer 
analysis  of  data  which  is  regularly  compiled 
would  develop  important  facts  which  are  not 
brought  out  in  the  routine  reports.  The  head  of  a 
department  may  desire  more  information  than 
that  regularly  furnished  him,  but  he  cannot  take 
the  time  to  get  it  himself,  and  a  clerk  could  not 
understand  its  meaning  or  application,  and  would 


Introduction  xi 

overlook  important  points.  Great  stress  is  laid 
on  the  comparison  of  results  for  successive  months, 
and  the  comparison  with  figures  for  the  corres- 
ponding months  of  the  previous  year,  but  statis- 
tics are  no  less  important  as  a  means  of  forecasting 
results  by  comparing  a  proposed  method  with  the 
one  in  practice.  The  great  expenditure  for 
statistics  is  relied  upon  to  show  the  leaks  and 
determine  wasteful  methods.  The  field  of  the 
statistician  should  be  broadened  and  he  should 
give  more  attention  to  the  possibility  of  con- 
structive activity.  The  statistical  department 
has  long  been  depended  upon  to  keep  costs  from 
going  up.  It  is  time  we  recognize  that  it  lies 
within  its  province  to  show  how  costs  can  be 
brought  down. 

Statistics  have  become  a  vital,  every -day 
need  not  only  in  transportation  but  also  in  indus- 
tries of  all  kinds,  in  finance,  in  journalism,  in 
social  work,  in  public  life,  and  in  business  of 
every  description.  They  are  necessary  to  men  of 
affairs,  publicists,  economists,  and  even  to  the 
average  citizen  if  the  significance  of  facts  anxi  the 
trend  of  events  are  to  be  comprehended.  Virtu- 
ally our  entire  political  life,  both  state  and  nation- 
al, is  now  regulated  and  its  course  determined  by 
statistics.  Every  important  branch  of  govern- 
ment has  its  statistical  bureaus.  Large  financial 
institutions,  industries,  manufactories,  railroads 
and  other  transi)ortation   (•omf)anics  have  their 


xii         Chartography  in  Ten  Lessons 

statistical  departments.  Innumerable  associa- 
tions must  resort  to  statistics  in  order  eflFiciently 
and  effectively  to  carry  on  their  work. 

This  recent  growth  in  the  demand  for  reliable 
statistics  and  their  correct  interpretation  has 
suddenly  raised  the  standing  of  the  statistician 
to  one  of  importance,  and  this  has  been  accom- 
panied by  a  corresponding  increase  in  his  remuner- 
ation. Today  the  openings  for  one  versed  in  the 
fundamental  laws  of  statistics — in  their  collection, 
compilation,  presentation,  and  interpretation — 
are  innumerable.  The  demand  is  greater  than  the 
supply. 

The  value  of  statistics,  while  great,  is  inestim- 
ably enhanced  by  the  aid  of  chartography.  It 
supplements  statistics — it  supplies  the  best  known 
method  for  their  presentation  and  interpretation. 
In  all  those  phases  of  presentation  which  count 
for  clearness  and  quickness  of  comprehension, 
no  other  method  is  equal  to  it.  It  makes  clear 
at  a  glance,  even  to  the  uninformed  and  unin- 
itiated, the  significance  and  tendency  of  the  fac- 
tors that  are  portrayed.  As  nine-tenths  of  the 
problem  in  interpretation  is  clear  presentation 
the  value  of  the  service  rendered  to  statistics 
by  chartography  cannot  be  over-emphasized. 
Especially  is  this  realized  when  it  is  remembered 
that  statistics,  to  be  useful  and  valuable,  must 


Introduction  xiii 

not  only  be  accurately  compiled  but  must  also  be 
correctly  interpreted.  Relatively,  too  much  time 
is  spent  in  the  collection  and  assembling  of  statis- 
tical material  and  too  little  in  its  clear  and  forcible 
presentation.  Here  is  where  chartography  be- 
comes an  invaluable  handmaid  to  statistics. 

The  graphic  presentation  and  interpretation 
of  statistics  as  the  basis  of  a  recognition  and  an 
miderstanding  of  industrial,  political,  financial, 
social,  economic,  and  other  tendencies  has  become 
essential  to  practical  men  of  affairs  as  well  as  to 
publicists,  economists,  and  others.  It  can  be 
made  of  incalculable  value  in  any  line  or  depart- 
ment of  business — in  that  of  finance,  corporate 
relations,  internal  organization,  traffic,  supplies, 
production,  prices,  wages,  costs,  and  scores  of 
others.  It  not  only  will  repay  its  cost  but  will 
be  found  of  such  great  value  in  so  many  ways 
that,  once  instituted,  it  will  never  be  abandoned. 
It  will  save  in  the  time  of  the  busy  executive  alone 
more  than  its  cost,  because  it  will  enable  him  to 
analyze  the  facts  and  tendencies  at  a  glance  in- 
stead of  spending  hours  in  studying  the  relations 
of  the  figures  in  the  different  columns.  It  will 
make  more  certain  the  correct  interpretation  of 
the  basal  information  necessary  to  action  and  the 
formulation  of  a  successful  policy.  It  will  en- 
large and  extend  his  individual  cxj)erience  and 


xiv        Chartography  in  Ten  Lessons 

his  accumulation  of  knowledge  of  the  details  and 
principles  of  his  business.  It  will  replace  vague- 
ness and  indefiniteness  by  assurance  and  certainty, 
hazy  conceptions  will  become  clear-cut  perspec- 
tives, and  these  in  turn  will  lead  to  a  compre- 
hensive grasp  of  the  entire  problem. 

The  recent  development  in  and  the  growing 
demand  for  diagrammatic  statistics  will  continue, 
and  he  who  masters  the  few  simple  yet  funda- 
mental laws  or  rules  upon  which  it  is  based  will  be 
in  a  position  to  become  an  authority  in  his  par- 
ticular field  and  to  command  a  comfortable  in- 
come. 

Frank  J.  Warne. 
Washington,  D.  C. 
October  1,  1919. 


LESSON  I 
Building  the  Chart 

Value  of  Table  of  Contents — Statistics  and 
Chartography — Definition  of  a  Chart — The 
Statistics — Horizontal  Lines — Vertical  Lines 
— A  Choice  of  Methods — The  Use  of  Pencil 
Dots — The  Framework. 

In  the  Table  of  Contents  preceding  this  Lesson 
has  been  given  a  comprehensive  outhne  of  the 
field  the  beginner  in  chartogra})hy  is  to  cover  in 
this  and  succeeding  pages.  It  is  a  bird's-eye 
view  of  the  course  of  study  that  has  been  mapped 
out  for  him  in  these  I^essons.  It  should  not  be 
passed  over  lightly  but  should  be  studied  seri- 
ously, for  the  reason  that  such  a  study  will  give 
to  the  student  at  the  very  outset  a  broad  per- 
spective of  the  problems  he  is  to  encounter  and 
overcome. 

Figuratively,  he  is  starting  on  a  mental  journey, 
with  its  ui)s  and  downs,  its  delights  and  i)lcasures, 
its  perplexities  and  obstacles— with  a  good  deal 
of  play  and  some  hard  work  aheaxl.  The  Table 
of  Contents  is  the  itinerary,  kej)t  by  one  who 
has  many  times  covered  the  same  ground  and 
who  thus  is  able  to  point  out  the  significance  of 

1 


2  Chartography  in  Ten  Lessons 

the  things  that  are  to  be  encountered.  The 
student  will  benefit  greatly  in  the  mastery  of 
these  Lessons  if  he  will  frequently  re-read  the 
Contents. 

VALUE  OF  TABLE  OF  CONTENTS 

The  Table  of  Contents  can  also  be  likened  to  a 
railroad  map  in  the  hands  of  one  starting  on  a 
long  journey.  It  enables  him  to  traverse  with 
his  eyes  the  entire  distance  of  the  trip,  noting 
the  general  characteristics  of  the  country  through 
which  he  is  to  pass,  its  mountains  and  rivers,  and 
the  principal  cities  along  the  way.  Thus  he 
secures,  before  he  starts  on  the  journey,  a  much 
better  idea  of  where  he  is  going  and  becomes  more 
familiar  with  the  country  through  which  he 
passes  than  he  would  if  he  studied  the  railroad 
map  piecemeal  after  the  journey  begins. 

These  ten  Lessons  will  take  the  student  on  an 
intellectual  trip  in  the  course  of  which  he  will  be 
called  upon  to  exercise  such  mental  traits  as 
application,  concentration,  observation,  and  im- 
agination in  overcoming  the  various  obstacles  on 
his  way  to  the  acquisition  of  knowledge  concern- 
ing the  art  of  chartograi)hy.  He  cannot  reach 
this  desirable  end  without  progressing  step  by 
step  in  mastering  its  various  features.  And  at 
every  step  in  this  progress  the  broad  view  of  his 


Building  the  Chart  3 

final  destination  which  he  will  have  acquired  by 
a  close  and  frequent  study  of  the  Contents  will  be 
of  material  assistance  to  him.  It  will  not  only 
enable  him  to  cover  the  ground  much  more 
quickly  and  with  less  exertion,  but  also  with 
much  more  satisfaction  to  himself. 

STATISTICS  AND  CHARTOGRAPHY 

The  value  and  usefulness  of  statistics  and  the 
relation  to  them  of  chartography,  as  well  as  the 
objects  of  chartography,  have  been  pointed  out 
in  the  Introduction.  From  a  reading  of  those 
pages  it  should  be  plain  that  figures  in  tabular 
form,  or  which  can  easily  be  arranged  in  the 
form  of  a  statistical  table,  are  essential  to  the 
drawing  of  a  chart — they  are  the  reason  for  the 
chart  being  made. 

DEFINITION  OF  A  CHART 

The  drawing  of  a  chart  therefore  presumes  the 
existence  of  the  statistics.  It  has  nothing  to 
do  with  their  collection  or  compilation.  A 
chart  is  merely  a  sheet  of  [)aper  on  which  tabu- 
lated facts  are  presented  graphically.  It  is 
also  called  a  diagram  or  "graph."  In  a  limited 
sense  it  can  bo  likened  to  a  moving  picture,  with 
this  difference:  In  the  case  of  the  chart  it  is  the 
eye  and  not  the  picture  that  moves. 


4  Chartography  in  Ten  Lessons 

the  statistics 

For  the  purpose  of  familiarizing  the  beginner 
with  the  various  steps  in  the  process  of  making 
the  framework  of  a  chart  these  figures  are  selected : 

1913      1914      1915      1916      1917      1918      1919 
26.7      26.7      26.4      28.1      38.2      49.5      57.2 

The  first  line  of  figures  represents  calendar 
years  and  the  second  line  the  average  retail  price 
of  a  pound  of  bacon  in  the  United  States  on 
April  15  of  each  specified  year.  This  information 
is  from  page  77  of  the  Monthly  Labor  Review  of 
the  Bureau  of  Labor  Statistics  of  the  United 
States  Department  of  Labor. 

To  make  a  chart  from  these  figures  is  a  simple 
proposition — as  simple  as  the  alphabet,  that  is, 
provided  one  knows  the  alphabet.  It  is  as  diflS- 
cult  to  one  who  does  not  know  how  as  the  alphabet 
is  to  the  child  first  beginning  to  lisp  the  letters. 
That  which  at  first  appears  to  be  a  very  com- 
plicated and  difficult  thing  to  do  comes  to  be 
surprisingly  simple  after  one  has  acquired  the 
necessary  knowledge  and  facility.  In  the  be- 
ginning all  that  is  needed  is  a  lead  pencil,  an 
ordinary  ruler,  and  a  blank  sheet  of  paper. 

HORIZONTAL    LINES 

A  glance  at  the  statistical  table  shows  there 


Building  the  Chart  '       5 

are  seven  prices  to  be  recorded.  These  can  be 
represented  for  the  present  by  as  many  lines 
drawn  with  the  lead  pencil  at  equal  distances 
apart  from  left  to  right  across  the  blank  sheet  of 
paper.  The  result  gives  the  lines  A-A,  B-B, 
C-C,  D-D,  E-E,  F-F,  and  G-G  on  this  page. 


These  are  horizontal  lines.  It  is  important 
that  the  beginner  bear  this  fact  in  mind.  He 
should  remember  th;it  u  horizon l:il  line  always 


6  Chartography  in  Ten  Lessons 

extends  in  the  direction  of  the  horizon,  that  is, 
parallel  to  the  horizon.  Here  the  horizon  is 
represented  by  the  top  edge  of  the  sheet.  Hori- 
zontal lines  are  drawn  from  left  to  right,  never 
from  right  to  left. 

VERTICAL    LINES 

In  our  statistical  table  we  have  another  set  of 
seven  figures.  These  represent  that  number  of 
years.  So  we  mark  off  on  the  bottom  horizontal 
line  G-G,  by  means  of  the  inch  and  its  fractional 
units  of  the  ruler,  seven  dots  each  an  equal  dist- 
ance apart,  the  first  dot  starting  at  the  beginning 
of  the  line  on  the  left.  These  dots  we  repeat  on 
the  top  horizontal  line  A-A.  Next  we  draw 
seven  vertical  lines  connecting  these  dots,  be- 
ginning with  the  first  dot  on  horizontal  line  G— G. 
Upon  completion  of  the  last  vertical  line  erase  the 
dots  on  the  top  and  bottom  horizontal  lines. 

Do  not  draw  these  vertical  lines  backward, 
that  is,  downward  from  line  A-A  to  line  G-G,  A 
vertical  line  is  an  upright  line,  that  is,  it  is 
directed  perpendicularly  to  the  plane  of  the  hori- 
zon, as  distinct  from  the  horizontal  line  which, 
as  has  been  said,  is  parallel  to  the  horizon. 
These  seven  vertical  lines  we  designate  as  H-H. 
I-I,  J-J,  K-K,  L-L,  M-M,  and  N-N.  Superim- 
posed on  the  seven  horizontal  lines  these  vertical 


Building  the  Chart  7 

lines  give  the  framework  shown  in  the  following 
drawing. 


HI  J  t*.  L  M  M 


The  distinction  between  horizontal  and  vertical 
lines  should  he  clear  to  tlic  .stiidoiit.  The  junc- 
tion of  a  horizontal  and  a  vertical  line  forms  a 
right  an^Ie. 


8  Chartograpiiy  in  Ten  Lessons 

Another  way  to  begin  the  erection  of  the  frame- 
work of  a  chart,  and  one  which  will  likely  appeal 
more  favorably  to  the  student  after  he  has  ac- 
quired greater  knowledge  of  the  subject,  is  to 
draw  first  the  horizontal  lines  G-G  and  A-A 
and  then  the  vertical  lines  H-H  and  N-N. 
This  gives  the  outline  on  the  opposite  page. 

These  four  lines  are  the  really  important  lines 
of  a  curve  chart.  In  relative  importance  they  are 
in  this  order:  H-H,  A-A,  G-G,  and  N-N.  The 
uses  to  which  each  is  put  the  student  will  become 
more  familiar  with  in  subsequent  Lessons.  All 
that  is  necessary  for  him  to  know  now  is  that: 

Line  H-H  is  the  vertical  scale  line  and  with  its 
units  of  measurement  virtually  determines  the 
distance  the  curve  is  to  move.  In  other  words, 
all  movements  of  the  curve  are  measured  by 
this  line. 

Line  A-A  is  the  horizontal  scale  line,  and  in 
all  curve  charts  involving  elements  of  time  it 
takes  the  time  units.  In  our  present  problem 
as  to  the  price  of  bacon  it  provides  positions  for 
the  years. 

Line  G-G  is  the  base  line  of  the  chart.  Figur- 
atively, it  is  the  foundation  line  upon  which  all 
the  vertical  lines  rest  and  from  which  they  start. 
This  base  line  is  the  zero  of  the  vertical  scale  and, 
whenever  possible,  should  always  be  indicated 


Building  the  Chart  9 

by  a  cipher.     All  movements  of  the  curve  are 
measured /rom  this  line. 

Line  N-N  is  the  least  important  of  these  four 


lines,  but  this  is  not  saying  that  it  is  not  necessary 
and  useful.  Its  functions  will  be  pointed  out 
to  the  student  later. 


10  Chartography  in  Ten  Lessons 

the  use  of  pencil  dots 

With  the  four  Hnes  I  have  described  already 
drawn  on  the  sheet,  the  beginner  next  divides 
by  dot  markings  the  base  line  G-G  into  six  equal 
spaces,  starting  the  first  of  the  five  dots  the  dis- 
tance of  one  space  from  the  left  end  of  the  base 
line  Gr-G  and  ending  the  dots  the  same  distance 
from  the  right  end  of  the  base  line.  Duplicate 
these  five  dots  at  their  respective  distance  apart 
on  the  top  line  A-A.  Now  connect  these  dots 
with  vertical  lines  extending  from  the  bottom  to 
the  top  line.  This  gives  the  five  lines  I-I,  J-J, 
K-K,  I^L,  and  M-M. 

Repeat  the  pencil  dots  with  the  same  space 
between  them  on  vertical  lines  H-H  and  N-N, 
beginning  the  first  of  the  five  dots  the  distance  of 
one  space  from  the  bottom  of  lines  H-H  and  N-N. 
Connecting  these  dots  with  horizontal  lines  gives 
the  lines  B-B,  C-C,  D-D,  E-E,  and  F-F.  Now 
erase  all  the  dot  markings.  The  result  is  the 
same  as  that  shown  on  page  7. 

THE  FRAMEWORK  OF  THE  CHART 

This  is  the  framework  of  the  chart.  It  is 
the  scaffolding  by  means  of  which  the  curve  is 
to  be  erected  or  constructed.  It  is  the  skeleton 
structure  for  supporting  the  curve.     Without  it 


Building  the  Chart  11 

the  curve  could  not  be  constructed  properly  or 
correctly;  neither  could  the  curve  adequately 
perform  the  service  for  which  a  chart  is  drawn. 
The  lines  will  be  found  to  occupy  positions  behind 
the  curve,  or  rather  to  form  a  setting  or  back- 
groimd  for  it.  The  framework  is  essential  for 
determining  the  movement  of  the  curve  and 
must  be  built  up  before  the  curve  can  be  placed. 


QUESTIONS  FOR  SELF-EXAMINATION 

1.  Describe  the  broad  view  of  the  field  of  chartography 
gained  from  a  study  of  the  Table  of  Contents.  What  ser- 
vice does  this  table  perform  for  the  student? 

2.  Describe  the  relation  between  chartography  and 
statistics. 

3.  Of  what  value  are  statistics  to  business?  To  other 
activities?     What  is  the  service  chartography  performs? 

4.  Do  these  Lessons  cover  the  entire  field  of  chartogra- 
phy?    Why? 

5.  Define  a  chart.  What  is  a  horizontal  line?  A  vertical 
line?     How  is  each  drawn  with  a  pencil? 

6.  What  is  the  framework  of  a  chart?  How  is  it  con- 
structed? 

7.  What  are  the  most  important  lines  of  the  framework? 
Describe  their  uses. 

8.  Of  what  use  are  pencil  dots  in  drawing  the  lines? 
How  are  these  dots  employed  in  laying  out  the  vertical  and 
horizontal  lines? 


12 


LESSON  II 

The  Scales 
Statistical  Variables — The  Independent  Vari- 
able— The  Dependent  Variable — The  Horizon- 
tal  Scale — Determining  the   Vertical   Scale — 
The  Scale  Lines — Reading  the  Scales — Plotting 
the  Statistics — The  Use  of  Gradicules. 
The  essence  of  a  chart  is  in  the  relation  which 
it  shows  exists  between  two  or  more  statistical 
elements.     Chartography  involves  a  comparison. 
Probably  the  most  frequent  comparison  is  that 
of  figures  representing  the  trend  or  tendency  of 
the  same  or  similar  element  or  factor  over  a 
period  of  time,  as  in  the  present  instance  of  our 
statistics  showing  the  average  price  of  bacon  on 
April  15th  of  different  years. 

STATISTICAL    VARIABLES 

This  price  is  not  the  same  for  all  the  years — 
it  has  the  capacity  of  changing  or  varying  with 
the  different  i)eriods  of  time.  Thus  in  relation 
to  each  other  these  two  groups  of  figures  are 
called  variables. 

Tin:   INDEPENDENT   VARIABLE 

A  comi)ari.s()n  })cing  involved,  one  or  the  other 
group  must  be  made  use  of  as  the  standard  by 
which  the  other  group  is  measured  or  interpreted. 

IS 


14  Chartography  in  Ten  Lessons 

The  group  so  used  becomes  the  independent 
variable.  Where  the  element  of  time  enters  into 
the  situation  it  is  nearly  always  the  standard  and 
thus  becomes  the  independent  variable. 

THE    dependent    VARIABLE 

The  statistical  group  that  is  to  be  measured 
or  interpreted  is  called  the  dependent  variable. 
In  our  present  problem  the  price  of  bacon  being 
dependent  upon  the  specified  periods  of  time  is 
the  dependent  variable. 

The  relation  between  or  the  tendency  of  the 
units  or  elements  of  the  dependent  variable  is 
measured  by  scales.  One  of  these  is  the  horizontal 
scale  and  the  other  the  vertical  scale.  Generally 
the  independent  variable  takes  the  horizontal 
scale.  This  fact  is  important,  as  a  great  deal  of 
confusion  results  from  a  violation  of  this  simple 
principle  of  chartography. 

"It  should  be  a  strict  rule  for  all  kinds  of  curve 
plotting,"  says  Brinton  in  his  Graphic  Methods 
for  Presenting  Facts,  "that  the  horizontal  scale 
must  be  used  for  the  independent  variable  and 
the  vertical  scale  for  the  dependent  variable. 
When  the  curves  are  plotted  by  this  rule  the 
reader  can  instantly  select  a  set  of  conditions 
from  the  horizontal  scale  and  read  the  informa- 
tion from  the  vertical  scale.     If  there  were  no 


The  Scales  15 

rule  relating  to  the  arrangement  of  scales  for  the 
independent  and  dependent  variables,  the  reader 
would  never  be  able  to  tell  whether  he  should 
approach  a  chart  from  the  vertical  scale  and  read 
the  information  for  the  horizontal  scale,  or  the 
reverse.  If  charts  are  always  plotted  with  the 
independent  variable  as  the  horizontal  scale, 
there  need  be  no  question  in  the  reader's  mind  as 
to  how  he  should  interpret  the  chart." 

THE    HORIZONTAL   SCALE 

Following  out  this  principle  of  chartography 
we  substitute  on  the  horizontal  line  A-A  of  the 
framework  on  page  7  (Lesson  I),  in  place  of  the 
letters  H,  I,  J,  K,  L,  M,  and  N,  the  figures  repre- 
senting the  years  in  our  statistical  table.  This 
gives  the  following  horizontal  scale  line: 

1913            1914            1915             1916            1917            1913            1919 
A  I 1 -J 1 1 J 1  A 

(H)  (I)  (J)  (K)  (L)  (M)  (N) 

DETERMINING   THE   VERTICAL   SCALE 

With  the  years  representing  the  horizontal 
scale,  the  average  price  of  bacon  figures — the 
dependent,  variable — must  necessarily  be  meas- 
ured   bv    the    vertical   scale.     Tlir    units   of   this 


16  Chartography  in  Ten  Lessons 

scale  are  determined  arbitrarily  by  figures  that 
must  have  a  spread  sufficient  to  include  the  lowest 
as  well  as  the  highest  price  of  bacon  that  is  to  be 
recorded  according  to  the  statistical  table.  The 
lowest  price  is  26.4  cents  in  the  year  1915  and  the 
highest  is  57.2  cents  for  the  year  1919. 

It  has  already  been  stated  that  the  lower  or 
base  horizontal  line  is  zero  and  should  be  indi- 
cated by  a  cipher.  This  also  means,  inasmuch 
as  the  vertical  lines  rest  upon  the  base  line,  that 
the  beginning  or  start  of  the  vertical  lines  must 
be  at  zero.  The  framework  above  the  base  or 
zero  line  G-G  on  page  7  (Lesson  I)  provides  six 
squares  within  which  the  highest  number — 
57.2 — of  our  statistical  table  has  to  be  recorded. 
With  these  facts  to  consider  it  is  a  simple  mathe- 
matical computation  which  shows  that  the  small- 
est unit  that  can  be  made  for  the  vertical  scale  is 
that  of  10  for  each  square.  Placing  this  unit 
from  0  to  60  on  the  vertical  scale  line  H-H  of 
the  framework  shown  on  page  7  (Lesson  I) 
instead  of  the  letters  G,  F,  E,  D,  C,  B,  and  A, 
gives  the  vertical  scale  on  opposite  page. 

THE    SCALE    LINES 

We  have  completed  both  the  horizontal  and 
vertical  scales  as  determined  by  the  figures  of  our 
statistical    table.     Substituting  these  scales   on 


The  Scales  17 

the  fralne-work  of  our  chart  in  place  of  the  letters 
designating  the  lines  gives  the  results  shown  on 
the  next  page. 

~H  These  scale  lines — the  horizontal  and 

^^'       *'^'    vertical — are  very  important  features 
of  a  chart ;  in  fact,  without  them  a  chart 
is  unintelligible.  They  must  be  adapted 
to  the  arbitrary  limitations  of  space, 
and  this  adaptation  is  readily  brought 
fQ)    about  by  increasing  or  decreasing  the 
space  allotted  to  each  unit  of  each  scale 
to  correspond  to   the  requirements  of 
(D)    the  particular  statistical  problem.    The 
vertical  scale  unit  itself  can  also  be  in- 
creased or  flecreased  as  the  particular 
problem  requires.    This  scale  measures, 
by  equal  distance  along  all  the  vertical 
,-.    lines,  the  units  of  the  variables  that  are 
being  charted — it  represents  by  space 
on  the  lines  of  the  chart  the  equivalent 
(G)    of  an  agreed  uj)on  element  of  the  statis- 
tics as  determined  by  the  units  selected. 

READING    THE    SCALES 

The  horizontal  scale  should  read  from  left  to 
right  with  the  earliest  year  to  be  recorded  a])|)ear- 
ing  first  and  the  remaining  years  following  con- 
secutively in  point  of  time. 


40 


30 


20 


10 


18 


Chartography  in  Ten  Lessons 


The  vertical  scale  beginning  at  zero  should 
read  upward  from  the  bottom  or  base  line  to 
the  top  or  horizontal  scale  line. 


60 


so 


AO 


30 


£0 


lO 


1913  1914  (915  1916  1917  1918  1919 


: 

572 

49.5 

36.2 

26  7 

26  7 

264 

28  1 

This  arrangement  "faces"  the  chart  to  the 
left.  A  chart  that  faces  to  the  right,  faces  in  the 
wrong  direction,  or,  putting  it  another  way,  a 


The  Scales  19 

chart  that  does  not  face  to  the  left  does  not  face 
in  the  "right*'  direction. 

PLOTTING    THE    STATISTICS 

We  are  now  prepared  to  begin  the  plotting  of 
the  statistics.  With  the  vertical  and  horizontal 
lines  drawn  the  proper  distance  apart  and  with  the 
figures  of  the  years  and  vertical  scale  units  cor- 
rectly indicated  by  lead  pencil  marks,  the  student 
next  begins  to  plot  on  the  respective  vertical 
lines,  by  means  of  pencil  dots,  the  exact  positions 
of  the  figures  of  the  statistical  table  as  determined 
by  the  vertical  scale. 

This  scale  applies  similarly  to  measurements  on 
all  the  other  vertical  lines  as  much  as  it  does  on 
the  vertical  scale  line  itself.  That  is,  any  unit  of 
the  vertical  scale  line,  say  30  of  our  present  scale, 
has  exactly  the  same  relative  position  on  all  the 
vertical  lines  as  it  has  on  the  vertical  scale  line. 

The  first  figure  of  our  statistical  table  that  is 
to  be  located  on  the  chart  is  26.7,  rci)resenting 
in  cents  the  average  price  of  a  pound  of  bacon 
on  April  l.O,  191'J.  The  first  vertical  line,  which 
is  our  vertical  scale  line,  also  represents  that  year, 
as  indicated  by  tlie  figures  1913  at  tiie  top  of  the 
line.  Starting  at  the  base  of  this  Hne  at  0  we 
proceed  upward  to   10,  to  20,  and  somewhere  be- 


20  Chartography  in  Ten  Lessons 

tween  this  unit  designation  and  the  next  one,  30, 
must  be  the  proper  location  for  the  figures  26.7. 

THE  USE  OF  GRADICULES 

It  is  easy  to  locate  where  25  should  be — midway 
between  20  and  30 — even  without  the  aid  of  the 
slight  projections  or  gradicules  which  have  been 
inserted  on  the  left  of  the  vertical  scale  line  in  the 
chart  on  page  18  for  the  purpose  of  aiding  the 
beginner.  Each  of  these  gradicules  represents 
one-tenth  of  the  vertical  scale  unit,  or  1,  and  there 
are  ten  gradicules  between  each  unit  of  10. 
They  perform  a  function  similar  to  the  sub- 
divisions of  the  inch  unit  on  the  ordinary  ruler — 
they  enable  the  student  to  locate  with  facility  on 
the  framework  any  figure  of  the  statistical  table 
that  falls  within  the  round  numbers  of  the  vertical 
scale  units. 

With  the  assistance  of  these  gradicules  it  is  a 
simple  matter  to  determine  the  correct  location 
on  the  vertical  scale  line  of  the  figures  26.7. 
This  is  indicated  by  means  of  a  pencil  dot.  The 
same  procedure  is  followed  in  locating  on  their 
respective  vertical  lines,  as  indicated  by  the 
vertical  scale,  the  remaining  figiu-es  for  each  of 
the  other  six  years  of  the  horizontal  scale. 

The  locating  of  each  number  on  each  vertical 
line  should  be  done  by  starting  at  the  base  or 


The  Scales  21 

zero  line  and  counting  upward,  and  not  by  start- 
ing from  the  position  of  the  preceding  pencil 
dot.  One  reason  for  this  is  to  prevent  the 
possibility  of  error  in  the  location  of  the  num- 
bers in  case  a  mistake  happens  to  be  made  in 
placing  the  first  one  on  the  vertical  scale  line. 
Besides,  it  is  important  that  the  beginner  should 
have  impressed  upon  his  mind  at  the  outset  that 
all  positions  of  numbers  charted  by  means  of  a 
curve  are  determined  in  relation  to  the  base  or 
zero  line.  This  is  clearly  indicated  on  page  18. 
On  this  drawing  the  numbers  represented  by  the 
pencil  dots,  and  which  are  those  of  our  statistical 
table,  are  placed  opposite  their  respective  dots 
to  emphasize  their  location. 

This  presentation  has  prepared  the  student 
for  the  actual  drawing  of  the  curve.  This  he 
does  by  starting  his  pencil  at  the  dot  on  the 
vertical  .scale  line  representing  the  number  20.7 
for  the  year  1913,  and  by  means  of  a  straight  line 
marks  the  space  l)etween  this  dot  and  the  dot 
representing  26.7  on  the  .second  vertical  line, 
which  latter,  according  to  the  horizontal  .scale, 
represents  the  year  1914.  It  so  happens  that  the 
average  j)ri(e  of  bacon  on  Ai)ril  1.5,  1914,  is 
identical  with  the  price  on  April  l.'i,  1913,  ac- 
cording to  our  statistical  table.  This  gives  a 
straight   line  connecting  vertical  lines   lf)l.S  and 


22 


Chartography  in  Ten  Lessons 


1914  at  the  point  26.7.  The  dot  on  the  vertical 
line  representing  the  year  1915  is  at  26.4,  this 
figure  being  the  average  price  of  bacon  on  April 
15  of  that  year.     The  student  connects  the  dot 


.    1913 
60 


50 


1914 


1915 


1916 


1917 


1918 


1919 


40 


30 


20 


10 


/ 

/ 

/ 

/ 

YEAR    CENTS 

/ 

1913  26.7 

1914  26.7 

1915  26.4 

1916  28.  1 

1917      38  2 

1918       495 

1919       57  2 

representing  26.7  for  the  year  1914  with  the  dot 
at  26.4  for  1915.  Continuing  this  process  for 
the  remaining  dots  gives  the  curve  shown  above. 


The  Scales  23 

In  this  drawing  the  lead  pencil  dots  have  been 
erased,  as  have  also  the  gradicules  along  the 
vertical  scale  line  shown  in  the  chart  on  page 
18,  these  dots  and  gradicules  being  of  no  further 
use.  The  figures  representing  the  price  of  bacon 
for  the  different  years  have  also  been  removed 
from  their  positions  opposite  the  dots  and  have 
been  placed  in  statistical  table  form,  with  the 
years  in  the  first  and  the  prices  of  bacon  in  the 
second  columns. 


QUESTIONS  FOR  SELF-EXAMINATION 

1.  What  is  the  essence  of  a  chart? 

2.  What  are  variables?  What  is  an  independent  varia- 
ble?    A  dependent  variable? 

3.  What  are  scales?  Describe  the  horizontal  scale.  The 
vertical  scale. 

4.  What  is  the  relation  between  the  variables  and  the 
scales? 

5.  What  scale  does  the  independent  variable  take? 
The  dependent  variable? 

6.  How  is  the  vertical  scale  determined? 

7.  What  is  the  base  line?  What  service  does  it  per- 
form? What  is  the  zero  line?  What  is  the  relation  between 
the  lower  horizontal  line  and  the  zero  line?  Between  the 
lower  horizontal  line  and  the  base  line? 

8.  What  is  a  square?  How  is  it  formed?  What  is  its 
function    in   chartography? 

9.  What  is  the  vertical  scale  unit?  How  is  it  deter- 
mined? 

10.  What  is  a  vertical  scale  line?  A  horizontal  scale 
line?  What  relation  to  these  are  the  vertical  and  hori- 
zontal scale  units? 

11.  How  should  the  horizontal  scale  be  read?  The  ver- 
tical scale?     In  what  direction  should  a  curve  chart  face? 

12.  What  is  meant  by  plotting  the  statistics?  How  is 
it  done? 

13.  What  is  the  relation  of  the  vertical  scale  units  to 
vertical  lines  other  than  the  vertical  scale  line? 

14.  What  are  gradicules?  Of  what  use  are  they  in  plot- 
ting the  statistics?  Where  are  they  located?  Of  what  use 
are  pencil  dots  in  plotting  the  statistics? 

15.  How  are  the  positions  of  the  figures  of  the  statistical 
table  on  the  framework  determined?  What  service  does 
the  zero  line  perform  in  this  determination? 

24 


LESSON  III 

The  Curve  Chart 

Making  the  Curve  Heavier — The  Horizontal 
Scale  Unit — Squares  Should  be  Equal — Effects 
of  Different  Scale  Units — Dropping  the  Zero 
Line — Indicating  the  Absence  of  the  Zero  Line 
— Divisors  for  the  Vertical  Scale. 

In  drawing  the  curve  remember  to  make  it 
heavier  than  any  other  line.  The  purpose  of 
this  is  to  have  it  stand  out  prominently  and  so 
catch  and  hold  the  eye  of  the  reader.  The 
curve  should  be  the  most  conspicuous  of  any 
line  on  the  chart  for  the  reason  that  it  embodies 
or  symbolizes  the  most  important  facts  that  are 
presented — it  is  the  whj'^  and  the  wherefore  of 
the  chart  being  called  into  existence.  Con- 
versely, the  framework  lines  making  up  the  back- 
ground of  the  chart,  that  is,  the  horizontal  and 
vertical  lines,  should  be  drawn  with  a  lighter 
touch  of  the  pencil  to  paper. 

The  curve  is  a  continuous,  unbroken  line,  and 
has  its  origin  at  the  j)oint  along  the  vertical  scale 
line  that  is  determined  for  the  time  or  other 
designation  of  that  line  by  the  statistics  and  the 
vertical  scale.  It  moves  across  the  page  from 
point   to  i)()itit   on   tlic  \'or(iral    lines    and  in  the 

25 


26  Chartography  in  Ten  Lessons 

direction  from  left  to  right  as  the  respective 
numbers  of  the  statistical  table  determine.  The 
curve  terminates  on  the  last  vertical  line  at  the 
point  the  statistics  require.  It  takes  the  shortest 
distance  between  two  points  and  generally  should 
approach  each  slantingly. 

THE  HORIZONTAL  SCALE  UNIT 

In  a  curve  chart  the  unit  of  the  horizontal 
scale  element — in  our  present  case  this  is  a 
calendar  year — marks  a  point  as  distinct  from 
space  between  points.  Each  vertical  line  pro- 
jects or  extends  its  horizontal  scale  unit  down- 
ward all  along  the  entire  distance  of  that  line 
even  to  the  base  or  zero  line.  The  curve  cannot 
and  does  not  affect  it — the  curve  does  not  move 
any  horizontal  scale  unit  a  hair's  breadth  from  its 
place  on  a  particular  vertical  line.  Or,  rather, 
the  horizontal  scale  unit  does  not  follow  the 
curve  from  its  point  of  contact  with  it  on  one 
vertical  line  to  the  point  of  contact  with  another 
horizontal  scale  unit  on  another  vertical  line. 
For  instance,  the  year  1913  ends  with  the  vertical 
line  so  designated  and  does  not  cover  the  space 
between  vertical  lines  1913  and  1914.  Quite 
commonly  in  curve  charts  this  distinction  is 
overlooked,  particularly  by  beginners,  and  the 
horizontal  scale  element  is  sometimes  made  to 


I 


The  Curve  Chart  27 

represent  space  on  the  horizontal  scale  line  and 
between  the  vertical  lines.     This  is  a  mistake. 

SQUARES  SHOULD  BE  EQUAL 

In  a  curve  chart  it  is  desirable  to  have  the 
curve  move  from  point  to  point  in  squares  or 
areas  of  equal  spacing  in  all  directions,  whether 
these  be  large  or  small.  This  means  that  both 
the  horizontal  and  vertical  scales  should  be  deter- 
mined upon  a  basis  that  will  permit  equal  spacing 
between  the  units  of  each  scale,  that  is,  between 
the  horizontal  lines  of  one  scale  and  the  vertical 
lines  of  the  other.  This  allows  the  curve  to  move 
up  or  down  and  from  left  to  right  an  equal  distance 
for  each  unit  of  measurement  of  both  scales. 

Many  curve  charts  are  being  made  in  which  this 
rule  is  violated.  It  must  bt  added,  however,  that 
the  observance  of  this  principle  is  not  always 
possible  owing  to  the  arbitrary  limitations  of 
space  and  to  the  necessities  of  the  scales.  The 
problem  for  the  chartographer  is  to  secure  as  accu- 
rate an  observance  of  this  rule  as  his  difficulties  will 
permit.  He  should  constantly  kcej)  in  mind  the 
important  fact  that  the  horizontal  and  vertical 
lines  are  made  u.se  of  to  measure  the  quantity  or 
volume  or  other  specified  quaUty  of  tiie  statistical 
element  that  is  charted,  and  that  these  rules  of 
measurement  should  be  as  fair  as  possible. 


28  Chartography  in  Ten  Lessons 

It  is  recommended  that  the  beginner  at  first 
draw  his  frame  work  or  scaffolding  lines,  both  hori- 
zontal and  vertical,  exactly  one  inch  apart,  thus 
giving  square  inches  within  which  the  curve 
moves.  Each  scale  will  then  have  its  units  of 
measurement  one  inch  distant  from  each  other. 
Later  on  the  student  can  practice  with  lessening 
or  lengthening  this  distance,  keeping  in  mind  not 
to  move  the  scale  units  to  points  less  than  one- 
half  inch  or  further  apart  than  one  and  one-half 
inches.  He  should  not  permit  the  units  of  either 
scale  to  be  separated  by  any  greater  distance  than 
the  units  of  the  other  scale. 

EFFECTS   OF   DIFFERENT   SCALE   UNITS 

The  student  should  also  practice  changing  the 
unit  of  the  vertical  scale  within  the  inch  square, 
increasing  or  decreasing  it  to  other  selected  units, 
in  order  to  observe  carefully  the  effects  these  dif- 
erent  units  have  upon  the  movement  of  the  curve. 
In  the  drawing  on  page  22  the  unit  is  10.  Let  us 
substitute  for  it  the  unit  5,  as  in  the  drawing  on 
the  opposite  page.  A  study  of  these  two  drawings 
will  disclose  a  number  of  important  differences. 

Probably  the  most  important  of  these  is  the  fact 
that  a  vertical  scale  unit  one-half  as  large,  other 
factors  remaining  the  same,  doubles  the  space 
within    which    the    curve    moves.       Conversely, 


The  Curve  Chart 


29 


doubling  the  scale  unit  decreases  by  one-half  the 
distance  the  curve  moves. 

This  space  in  the  drawing  on  page  22  requires 


1913             1914            1915            1916            I9l7            1918            19 

60 
55 
50 
45 
40 
35 
30 

/ 

/ 

1 

■>c. 

vertically  a  fraction  more  tliaii  three  of  the 
squares — the  spread  in  tlic  difrcronce  between 
the  lowest  and  highest  numbers  of  the  statistical 


30  Chartography  in  Ten  Lessons 

table  is  30.5  and  with  10  as  the  unit  this  leaves 
.5  more  than  three  times  10.  In  the  drawing 
on  the  preceding  page  the  vertical  scale  unit  5 
requires  a  fraction  of  .5  more  than  six  times  5  to 
accommodate  the  curve,  or  seven  vertical  squares 
at  the  very  least.  As  the  drawing  on  page  22 
provides  only  six  squares,  another  one  has  to  be 
added  to  the  framework,  as  is  done  on  the  page 
preceding.  This  is  accomplished  by  inserting  an 
additional  horizontal  line,  either  above  the  top  or 
below  the  bottom  horizontal  line,  and  then  extend- . 
ing  to  it  all  the  vertical  lines. 

With  the  new  vertical  scale  unit  being  5  and 
with  the  highest  number  to  be  charted  being 
57.2  for  the  year  1919,  a  square  must  be  provided 
for  each  of  the  units  of  5  if  the  scale  is  to  begin  at 
zero.  This  demands  at  least  twelve  squares  for 
the  vertical  scale  from  0  to  60.  But  it  is  physically 
impossible  to  accommodate  this  many  squares 
of  the  present  size  within  the  space  limitations. 

DROPPING   THE   ZERO   LINE 

The  next  step  is  to  ascertain  from  the  statis- 
tical table  the  lowest  number  to  be  recorded. 
This  is  26.4  for  1915.  It  is  clear  from  this  that 
the  space  occupied  by  all  the  squares  below  the 
vertical  scale  unit  25  will  not  be  needed  for  record- 
ing the  movement  of  any  part  of  the  curve,  for 


The  Curve  Chart  31 

in  not  a  single  year  of  all  the  seven  given  in  the 
statistical  table  does  the  price  of  bacon  fall  below 
that  unit.  Consequently,  beginning  the  vertical 
scale  at  25  instead  of  at  0  permits  the  elimination 
from  the  framework  of  five  squares.  The  number 
that  remains,  which  is  seven,  is  sufficient  for  the 
requirements. 

It  has  been  made  clear  in  preceding  Lessons 
that  the  bottom  horizontal  or  base  line  of  a  curve 
chart  represents  zero  of  the  vertical  scale  and  is 
indicated  by  a  cipher  as  follows: 


INDICATING    THE    ABSENCE    OF    THE    ZERO    LINE 

Such  a  line,  of  course,  cannot  possibly  be  used 
as  the  base  line  with  the  unit  of  our  vertical  scale 
starting  at  25,  so  the  zero  designation  is  omittt^d. 
Attention  should  always  be  called  to  this  omis- 
sion on  the  chart  itself  and  this  can  be  done  by 
inserting  directly  below  the  base  line,  with  its 
proper  unit  designation,  a  faint  line  of  dashes  or 
one  of  dots,  or  a  wavy  or  slightly  undulating 
line,  as  indicated  on  th(!  next  page.  Rulers  pro- 
vided  with  these  undulations  can  be   |)ur(hjised. 


32  ClIARTOGRAPHY   IN   TeN   LesSONS 


The  student  should  keep  in  mind  as  a  general 
principle  the  fact  that  the  vertical  scale  begins 
on  the  base  line  at  0,  although  he  will  frequently 
find  that  this  is  physically  impossible  because  of 
the  nature  of  his  statistical  problem.  This  pre- 
vails more  often  among  large  numbers  than  with 
percentages.  Usually  the  lowest  nu  nber  to  be 
charted  starts  at  a  point  so  high  above  0  that  the 
space  required  to  show  the  latter  on  the  chart  is 
out  of  all  proportion  to  that  necessary  to  in- 
dicate the  movement  of  the  curve.  Again, 
frequently  in  such  cases  the  vertical  scale  unit 
determined  by  including  zero  becomes  so  large 
that  fluctuations  in  the  movement  of  the  curve 
reflecting  the  trend  of  the  statistics  (which  fluc- 
tuations would  be  made  clear  by  the  use  of  a 
smaller  unit)  are  smoothed  out  or  flattened  so 
that  that  which  should  be  a  curve  approaches 
nearer  to  a  straight  line.  Thus  it  is  not  always 
possible  to  plot  a  curve  chart  so  that  the  zero  of 


The  Curve  Chart  33 

the  vertical  scale  will  be  shown  and  at  the  same 
time  clearly  present  the  trend  of  the  statistics, 
which  latter  is  the  primary  object  of  the  curve. 

In  beginning  to  read  a  curve  chart,  among 
the  first  things  to  be  observed  is  whether  the 
vertical  scale  starts  at  zero  and  if  it  does  not  to 
make  proper  alloAvance  for  this  fact  in  the  inter- 
pretation of  the  movement  of  the  curve.  Unless 
this  is  kept  in  mind  an  erroneous  idea  or  impres- 
sion of  the  extent  of  the  movement  will  result. 
A  chart  that  does  not  present  the  zero  line  and 
fails  to  call  attention  to  the  omission  in  the 
ways  indicated,  or  neglects  similar  precautions, 
is  constructed  in  error.  Such  a  chart  is  very 
likely  to  be  misleading  no  matter  how  excellent 
or  perfect  its  other  features  may  be. 

DIVISORS    FOR   THE   VERTICAL   SCALE 

The  selection  of  the  vertical  scale  unit  is  thus 
not  without  its  difficulties.  The.se  the  student 
will  learn  to  overcome  as  his  experience  with 
varying  stiitistical  problems  increases.  He  will 
learn,  among  other  things,  that  particular  numeri- 
cal divisors  are  more  advantageous  as  imits  than 
some  of  the  others. 

The  divisor  .'J,  for  instance,  is  an  awkward  and 
inconvenient  s<-alc  unit,  not  only  for  compniing 
on   the  vertical   lines  the  measurements  of   the 


34  Chartography  in  Ten  Lessons 

statistical  element  but  also  for  calculating  by 
the  interpreter  of  the  chart.  The  divisor  2  is 
much  better,  and  5  and  10  are  nearly  always  ideal. 
Such  units  as  3,  4,  6,  7,  8,  and  9  are  not  as  good  as 
2,  5,  10,  20  and  so  on,  the  latter  group  being  more 
easily  divisible  into  the  spaces  along  the  vertical 
lines  as  well  as  into  the  numbers  of  the  statistical 
table. 

Whatever  scale  unit  is  selected  it  must  permit 
the  inclusion  within  the  arbitrary  limitations  of 
the  framework  of  the  smallest  as  well  as  the 
largest  number  that  is  to  be  charted.  The  unit 
must  be  such  as  to  permit  of  a  spread  between  the 
lowest  and  highest  numbers  charted  sufficient  to 
bring  out  clearly  in  the  curve  the  points  or  tend- 
ency to  show  which  the  particular  chart  has  been 
designed;  at  the  same  time  it  must  not  be  too 
small  as  to  result  in  exaggeration.  It  is  as  serious 
an  offense  to  exaggerate  with  curves  as  it  is  with 
words.  Accuracy  in  chart  expression  is  as  im- 
portant as  is  the  use  of  words  in  expressing 
thought,  and  the  various  uses  or  functions  of  the 
vertical  scale  unit  have  much  to  do  with  accuracy 
in  curve  charts. 

On  a  finished  chart  the  student  will  not  find 
any  dots  and  similar  marks  used  as  guides  in 
erecting  the  scaffolding  of  the  framework,  which 
means  that  all  such  marks  must  be  erased  from 


The  Curve  Chart  35 

the  completed  chart.  He  will  find,  however, 
that  all  the  vertical  and  horizontal  lines  make 
complete  right  angles  at  all  points  of  junction; 
that  all  such  lines  are  straight  lines;  that  they 
form  accurate  squares;  that  the  curve  is  slightly 
heavier  than  the  other  lines;  that  the  scale  unit 
figures  are  in  their  correct  positions  in  relation 
to  their  respective  lines;  and  that  the  horizontal 
and  vertical  scale  unit  figures  do  not  crowd  the 
lines  but  are  separated  from  them  by  the  correct 
spacing. 


QUESTIONS  FOR  SELF-EXAMINATION 

1.  Why  is  the  curve  made  heavier  than  other  lines? 

2.  Define  a  curve.  How  is  it  emphasized  in  comparison 
with  the  horizontal  and  vertical  lines? 

S.  Define  the  horizontal  scale  unit.  What  function  does 
the  vertical  scale  lines  perform  for  this  unit?  What  is  the 
relation  of  the  curve  to  it? 

4.  What  effect  have  unequal  squares  on  the  movement 
of  the  curve?  What  relation  is  there  between  the  squares 
and  the  scale  units? 

5.  What  are  some  of  the  effects  of  changing  the  vertical 
scale  unit? 

6.  When  is  the  zero  line  omitted?  How  is  this  omission 
indicated? 

7.  Explain  the  reasons  for  omitting  the  zero  line. 

8.  What  effect  has  the  omission  of  the  zero  line  on  the 
reading  of  the  curve? 

9.  What  are  numerical  divisors?  When  and  how  are 
they  used?     What  ones  are  better  than  others? 

10.  What  must  the  divisors  provide  for? 


36 


LESSON  IV 

Features  of  a  Complete  Chart 

The  Statistical  Table — Table  Should  Appear 
on  Chart — The  Make-up  of  the  Table — Spac- 
ing the  Columns — The  Form  of  the  Table — 
Duplicating  the  Scale  Units — The  Place  for 
the  Horizontal  Scale — Word  Designation  of  the 
Scale— The  Title— The  Foot-Notes—The  Neat 
Lines. 

The  drawing  on  page  38  is  a  complete  curve 
chart  constructed  according  to  the  instructions 
of  the  preceding  Lessons.  The  student  should 
examine    carefully    every    one    of    its    features. 

Particular  study  should  be  given  by  the  student 
to  the  statistical  table.  It  occupies  the  position 
in  the  lower  right  hand  corner  of  the  drawing  on 
page  22  (Lesson  II)  but  in  the  accompanying 
chart  it  is  located  in  the  upper  left  hand  corner. 
In  each  case  the  location  of  the  table  is  adapted 
to  the  requirements  of  the  particular  chart  and 
each  is  correctly  placed.  It  will  be  found  that 
one  or  the  other  of  these  two  j)ositions  is  usually 
the  place  for  the  table,  the  lower  left  hand  corner 
and  the  upper  right  hand  corner  nearly  always 
being  required  for  the  free  and  unobstructed 
movement  of  the  curve. 

87 


I) 


38 


Chartography  in  Ten  Lessons 


THE  AVERAGE  PRICE* OF   BACON 

UNITED  STATES,    I9I3-I9I9 

CENTS 

1913 

1914            1915            1916            1917           1918 

1919 

55 

/ 

60 

55 

YEAR   CElhTS 

1913      26  7 

1914      26  7 

50 

1915      264 

50 

1916     28.1 

t 

1917     38.2 

/ 

45 
40 

1918  49.5 

1919  57.2 

/ 

45 
40 

/ 

/ 

35 

/ 

35 

/ 

30 

/ 

30 

/ 

25 

25 

19 

13 

1914          1915           1916          1917           1918 

1919 

srartstics 

»r«   f/-em  Monrtily  U&bOf-   »«vl«.*w.  p.  77,                                    ■•  AvmrAQ«  p*-icm 

.s  or 

This  simply  means  that  there  is  no  arbitrary 
position  on  the  chart  for  the  statistical  table  but 
that  its  location  is  determined  by  the  result  of 
the  plotting  of  the  curve.  The  only  general  rule 
to  follow  is  to  place  the  table  of  figures  in  the 


Features  of  a  Complete  Chart        39 

particular  position  on  the  chart  that  disi)lays  it 
to  the  best  advantage  without  at  the  same  time 
crowding  the  scale  lines  or  interfering  with  the 
curve.  Breaking  the  vertical  lines  1914  and  1915 
and  the  horizontal  lines  45,  50,  and  55,  as  is  done 
in  the  accompanying  chart,  is  not  objection- 
able but  rather  advisable  in  preference  to  these 
lines  extending  through  and  breaking  up  the  table. 
"Boxing"  the  two  colunms  of  the  table  with 
light  lines,  as  in  the  accompanying  chart,  adds  to 
the  neat  appearance  of  the  finished  diagram. 

TABLE    SHOULD   APPEAR   ON    CHART 

Virtually  every  chart  is  based  upon  statistical 
information.  Usually  this  information  is  in  the 
form  of  a  statistical  table  or  columns  of  figures. 
If  the  chart  has  been  properly  constructed  and  if 
the  figures  of  the  table  are  correct,  the  presence 
of  the  statistics  is  not  essential  to  a  complete 
understanding  of  the  chart — its  meaning  will 
be  clear  without  the  figures.  Nevertheless  it  is 
highly  important  in  good  chart  making  that  the 
statistics  upon  which  the  diagram  is  based  should 
occupy  an  inifjortant  f)]ace  on  the  chart. 

This  reproduction  of  tlic  figures  furnishes  proof, 
if  proof  is  needed,  of  the  correctness  of  the  move- 
ment of  the  curve  as  shown  in  the  chart  and  will 
also  be  of  service  to  those  who  may  wish  to  u.se  the 


40  Chartography  in  Ten  Lessons 

data  in  other  directions  or  to  make  different  com- 
pilations. Unless  the  statistics  from  which  the 
chart  is  made  are  shown  upon  it  there  is  no  easy 
way  to  check  up  the  work  of  the  chartographer. 

THE   MAKE-UP   OF   THE   TABLE 

The  internal  make-up  and  arrangement  of  the 
statistical  table  also  require  some  thought  from 
the  student.  Its  construction  would  appear  at 
first  glance  to  be  an  easy  thing  to  do  and  yet  the 
task  has  its  difficulties. 

All  the  numbers  of  the  same  statistical  element 
that  are  to  be  compared  should  be  placed  in  the 
same  vertical  column  one  under  the  other  and  not 
too  far  apart,  the  digits  of  the  tens  and  hundreds 
and  so  on  occupying  their  proper  positions  in 
relation  to  similar  digits  of  other  numbers  in  the 
same  column.  In  the  case  of  years,  these  are  ar- 
ranged vertically  and  in  proper  sequence  of  time 
one  under  the  other  with  the  earliest  year  at  the 
top  and  the  latest  year  at  the  bottom  of  the  col- 
umn. Nearly  always  the  years  are  in  the  first 
column  to  the  left  in  a  table  of  two  or  more  col- 
umns. Vertical  columns  of  figures  read  downward 
from  the  top  and  never  upward  from  the  bottom. 
This  is  in  inverse  order,  it  will  be  noted,  to  the 
eading  of  the  vertical  scale  units. 

Each  column  has  its  proper  word  designation 


Features  of  a  Complete  Chart        41 

just  above  the  first  number,  as  years  and  cents  in 
the  table  of  the  chart  on  page  38.  This  is  the 
column  heading.  The  space  for  it  is  usually  very 
limited  and  for  this  reason  it  should  be  confined  to 
simple  words  of  the  fewest  possible  letters  con- 
sistent with  clearness  as  to  the  meaning  of  the 
column  of  figures.  Double  meaning  of  words 
should  be  as  carefully  guarded  against  as  indefin- 
iteness  in  meaning,  each  being  a  serious  offense 
against  clearness  of  expression.  \Mien  two  or 
more  words  are  necessary  in  the  heading  of  a 
column  it  is  usually  advisable  to  make  of  them 
two  or  more  lines  just  above  the  first  number, 
with  each  word  having  a  line  to  itself  instead 
of  all  the  words  occupying  a  single  line,  which 
latter  nearly  always  extends  the  heading  too  far 
on  either  side  of  the  column  of  figures, 

SPACING    the   columns 

Where  two  or  more  columns  of  figures  are  in 
the  same  table  attention  has  to  be  given  to  the 
proper  si)acing  between  the  columns  as  well  as 
l)etween  the  luimbers  themselves  and  their 
headings.  Hut  in  every  table  the  number  of 
columns  should  be  strictly  limited  to  the  fewest 
possible  for  the  purpo.se  in  view,  the  inclusion  of 
any  that  are  not  necessary  detracting  from  the 
emphasis   tliat    must   be  given    to   the  princii)al 


42  Chartography  in  Ten  Lessons 

facts  and  tendencies  shown  by  the  statistics.  The 
table  raust  be  complete  in  itself,  however,  with  no 
vitally  important  factor  missing.  To  this  end 
more  than  one  comparison  should  not  be  at- 
tempted in  the  same  table. 

The  form  of  the  table  has  to  be  adjusted  not 
only  to  the  size  of  the  chart  but  in  particular  to 
the  space  available  on  the  framework  for  its 
presentation  without  interfering  with  the  curve. 
Interference  by  the  table  with  the  light  horizontal 
and  vertical  lines  is  not  so  important;  nor  is  a 
correct  interpretation  or  reading  of  the  curve 
interfered  with  even  when  the  vertical  scale  line  is 
broken  into  by  the  table  at  points  which  the  curve 
does  not  approach. 

THE   FORM   OF   THE   TABLE 

There  are  distinct  forms  best  adapted  to  par- 
ticular purposes  with  which  the  student  will  be- 
come familiar  only  by  practice.  He  will  have  to 
decide  at  times  whether  he  will  include  all  his 
data  in  one  table  or  break  them  up  into  two  or 
more  tables  with  a  chart  to  illustrate  each.  Com- 
pactness as  well  as  proximity  of  the  numbers  for 
comparative  purposes  are  advantages  which 
must  sometimes  be  surrendered  at  the  demand  of 
more  pressing  requirements.  If  the  table  is  too 
large  confusion  to  the  eye  results  and  diflBculty  is 


Features  of  a  Complete  Chart        43 

encountered  in  following  the  significance  of  the 
separate  columns.  Interpretation  also  is  particu- 
larly taxing  if  the  tabulation  is  dealing  with  a 
complex  mass  of  figures. 

SIMPLICITY  THE  GUIDING  RULE 

If  the  student  will  keep  in  mind  that  simplicity 
must  be  the  guiding  rule  he  will  usually  not  go  far 
WTong  in  his  decisions.  Much,  of  course,  depends 
upon  the  data  that  must  be  shown  but  quite  often 
more  can  be  eliminated  from  the  columns  than 
at  first  seems  possible.  Foot-notes  as  explanations 
of  the  table  often  show  a  way  out  but  these  should 
be  kept  at  the  minimum.  A  title  to  the  table 
separate  from  that  of  the  chart  is  imnecessary. 

Sometimes  the  exigencies  of  space  limitations 
combine  with  the  requirements  of  the  movement 
of  the  curve  to  prevent  the  use  of  the  form  of 
statistical  table  that  has  been  described  and  which 
is  shown  in  the  chart  on  i)age  38.  In  such  cases 
recourse  has  to  be  had  to  sonic  other  form,  some- 
times to  that  shown  on  page  4  (Lesson  I)  with 
the  years  and  prices  of  bacon  arranged  in  hori- 
zontal lines  instead  of  vertical  columns.  At 
times  when  this  form  has  to  be  resorted  to  it  is 
not  possil)le  to  place  the  table  within  the  frame- 
work and  in  such  cases  a  position  has  to  be  found 
for  it  elsewhere  on  the  chart. 


44  Chartography  in  Ten  Lessons 

duplicating  the  scale  units 

In  the  chart  on  page  38  the  unit  figures  of  the 
horizontal  scale  have  been  placed  on  both  the  top 
and  bottom  lines  and  those  of  the  vertical  scale 
on  both  the  first  and  last  vertical  lines.  This 
arrangement  has  many  advantages.  While  it 
is  not  essential  to  the  reading  of  the  curve,  at 
the  same  time  it  facilitates  the  interpretation  of 
its  movement  in  that  the  reading  of  the  prices 
of  bacon  for  the  first  and  immediately  succeeding 
years  is  permitted  without  requiring  the  eyes  to 
move  upward  to  observe  these  horizontal  scale 
units;  also,  it  permits  the  quick  reading  of  the 
prices  of  bacon  for  1919  and  the  immediately 
preceding  years  without  requiring  the  eyes  to 
travel  across  the  page  to  observe  these  particular 
vertical  scale  units.  The  scale  units  arranged 
along  all  four  sides  also  serve  to  give  a  border- 
like appearance  to  the  framework  and  introduce 
a  little  greater  uniformity  in  place  of  a  tendency 
towards  a  lack  of  balance. 

THE  PLACE  FOR  THE  HORIZONTAL  SCALE 

Some  chartographers  prefer  placing  the  hori- 
zontal scale  units  along  the  bottom  line  only. 
My  own  preference  is  that  where  they  are  to 
appear  only  once  on  the  chart  then  the  place 


Features  of  a  Complete  Chart        45 

for  them  is  on  the  top  line.  That  Hne  will  be 
found  to  be  much  more  convenient  as  the  hori- 
zontal scale  line;  besides,  there  are  other  im- 
portant uses  for  the  bottom  horizontal  line,  such 
as  serving  as  the  base  line  and  as  the  zero  line. 

This  preference  is  influenced  also  as  the  result 
of  more  than  ten  years'  experience  in  chart 
making  for  practical  commercial  purposes.  Dur- 
ing this  experience  it  has  been  observed  that  most 
people  in  reading  a  chart  start  at  the  top  with 
the  title  and  glance  downward.  With  the  units 
of  the  horizontal  scale  on  the  top  line  the  reader 
early  in  the  process  of  interpretation  is  informed 
of  these  important  facts  which  he  must  know  if  he 
is  to  read  the  chart  intelligently  and  correctly. 

Placing  the  horizontal  scale  units  on  the  bottom 
line  meets  with  the  objection  that  the  space 
beneath  this  line  is  usually  needed  in  most  curve 
charts  for  inii)ortant  explanations  and  foot- 
notes, such  as  credit  for  the  source  of  the  statis- 
tical information  upon  which  the  chart  is  built, 
notice  of  coi)yright,  and  so  on.  With  the  hori- 
zontal scale  figures  also  there  that  section  of  the 
chart  is  likely  to  give  the  ai)pearance  of  crowding. 
Again,  with  the  horizontal  scale  ligures  located 
on  the  bottom  line  I  have  frequently  encountered 
practical  difficulties  hard  to  overcome  because 
the  first  and  last  of  these  units  interfere  with 


46         Chartography  in  Ten  Lessons 

those  of  the  lowest  scale  measurement  of  the 
vertical  lines,  both  sets  of  figures  being  located 
at  nearly  the  same  point  of  the  right  angles  formed 
by  these  vertical  and  horizontal  lines.  As  op- 
posed to  this,  it  is  nearly  always  possible  to  extend 
the  upper  part  of  the  framework  at  least  one 
series  of  squares  beyond  the  highest  point  to  be 
recorded  by  the  vertical  scale  and  this  permits 
the  figures  of  the  horizontal  scale  units  to  have  a 
line  all  to  themselves  without  interfering  with  and 
without  interference  from  any  of  the  figures  of  the 
vertical  scale. 

There  is  no  objection,  of  course,  to  reproducing 
the  horizontal  scale  figures  on  the  bottom  line 
whenever  there  is  room  for  them,  and  this  prac- 
tice is  recommended  as  being  advantageous, 
especially  in  charts  of  unusual  depth,  as  it  facili- 
tates a  quick  reading  of  the  curve  movement. 

WORD  DESIGNATION  OF  THE  SCALE 

Further  assistance  in  the  interpretation  of  the 
chart,  and  especially  in  the  reading  of  the  curve, 
is  rendered  if  the  primary  characteristic  of  the 
statistical  element  represented  by  the  vertical 
scale  is  indicated  by  a  word  designation  just 
inside  the  top  border  line  and  directly  above  the 
center  of  the  horizontal  scale  line.  This  is  shown 
in  the  designation  "Cents"  in  the  chart  on  page 


Features  of  a  Complete  Chart        47 

38.  Such  a  designation  states  concisely  to  the 
reader  what  the  vertical  scale  figures  represent — 
it  explains  the  essence  of  the  curve.  Its  value 
and  usefulness  will  be  impressed  upon  the  student 
as  he  progresses  in  his  studies. 

THE  TITLE 

Another  important  matter  to  be  considered 
before  our  chart  is  a  complete  one  is  the  title  or 
heading.  Every  chart  must  have  a  title.  With- 
out it  the  chart  is  almost  as  incomplete  as  it 
would  be  if  the  curve  itself  were  omitted.  The 
title  is  as  much  a  part  of  the  chart  as  are  the 
scale  lines  or  table  of  statistics.  It  is  more  im- 
portant than  the  beginner  in  chart  making  is 
apt  to  realize. 

The  title  should  not  contain  a  single  unneces- 
sary' word.  The  space  for  it  is  usually  limited 
and  too  many  words  detract  from  the  effect  in 
expressing  the  idea  intended.  Simple  words  of 
one  syllable  are  preferable.  This  choosing  of 
words  in  the  selection  of  a  title  is  a  splendid 
exercise  in  enabling  one  to  secure  a  better  com- 
mand of  the  P^nglish  language  and  in  compre- 
hending more  clearly  himself  the  essence  of  the 
chart.  The  title  should  be  so  clear  in  its  meaning 
that  misinterpretation  is  impossible,  and  so  com- 
prehensive in  its  scope  as  to  cover  all  the  unport- 


48  Chartography  in  Ten  Lessons 

ant  data  presented  by  the  chart  so  that  the  inter- 
preter will  not  have  to  look  elsewhere  for  explana- 
tion. This  is  not  always  possible  and  in  such 
cases  a  foot-note  explanation  at  the  bottom  of  the 
chart  is  advisable.  Indefiniteness  in  title  mean- 
ing is  a  serious  offense.  Similar  statements  are 
equally  applicable  to  any  sub-title. 

The  position  of  the  title  is,  of  course,  at  the 
top  or  head  of  the  chart,  as  shown  on  page  38. 
The  best  title  is  one  comprising  a  single  line  but 
this  is  not  always  easy  to  accomplish.  In  the 
chart  referred  to  it  has  been  found  necessary  to 
have  two  lines  in  the  title,  and  in  such  cases  the 
letters  of  the  words  in  the  second  line  should  be 
slightly  smaller  than  those  of  the  first  line.  The 
principal  idea  in  this  chart  is  the  tendency  in  the 
price  of  bacon,  so  its  title  becomes  "The  Average 
Price  of  Bacon."  But  as  this  does  not  give  the 
information  quite  complete  enough,  the  reader  is 
told  in  the  second  line  that  the  price  is  for  the 
entire  "United  States"  and  for  the  years  "1913 
to  1919."  The  asterisk  after  the  word  "price" 
refers  the  reader  to  the  foot-notes,  where  it  is 
stated  that  the  average  price  given  is  of  April 
15  of  each  year. 

THE    FOOT-NOTES 

The  place  on  the  chart  for  the  foot-notes  is 


Features  of  a  Complete  Chart        49 

just  below  the  base  line  and  outside  the  frame- 
work proper.  These  serve  a  useful  purpose  in 
presenting  descriptive  information  sometimes 
necessary  to  clear  up  a  point  that  has  not  been 
brought  out  sufficiently  in  the  chart,  as  indicated 
in  the  use  of  the  asterisk  in  the  chart  on  page  38. 
In  the  foot-notes  there  should  always  be  a  state- 
ment as  to  the  source  of  or  authority  for  the 
statistics  upon  which  the  chart  is  based.  This 
is  shown  on  the  chart  just  referred  to  by  the 
notation  "Statistics  are  from  Monthly  Labor 
Review,  p.  77,  U.  S.  Bureau  of  Labor  Statistics." 
The  foot-notes  also  supply  a  convenient  place  for 
the  legal  statement  required  in  case  the  chart  is 
copyrighted. 

THE    NEAT    LINES 

With  the  drawing  of  the  border  or  "neat"  lines, 
one  on  each  side  of  the  framework  and  usually 
about  one-half  an  inch  from  the  horizontal  and 
vertical  scale  lines,  tlie  chart  is  completed.  These 
neat  lines  give  a  sort  of  frame  to  the  chart,  as 
shown  on  page  38. 

In  a  good  curve  chart  tlie  principal  conclusions 
to  be  drawn  from  tlie  statist ical  table  are  made 
plain,  all  doubt  as  to  the  tendency  or  course  of  the 
phenomena  r«'j)rcscrit('<l  by  the  nnnibers  is  re- 
moved, and  all  possible  errors  have  been   elimi- 


50  Chartography  in  Ten  Lessons 

nated.  This  ability  to  analyze  the  significance 
of  a  table  of  statistics,  to  interpret  the  results 
correctly  and  clearly,  and  to  indicate  the  con- 
clusions lucidly  and  succinctly  is  one  of  the 
characteristics  of  chartography.  The  results 
disclosed  by  a  curve  based  upon  a  statistical  table 
quite  often  reveal  at  a  glance  important  facts 
that  could  not  have  been  known  except  from 
considerable  study  of  the  figures  by  an  expert. 
Usually  an  accompanying  explanation  or  analysis 
is  unnecessary.  If  so  the  chart  has  failed  of  its 
primary  purpose. 

The  task  of  checking-up  is  not  optional  with 
the  student;  it  is  compulsory — he  not  only  should 
but  he  must  go  over  carefully  each  chart  from  top 
to  bottom. 

If  it  is  a  curve  chart,  do  all  the  horizontal  scale 
units  center  on  the  end  of  the  vertical  lines.'* 

Are  the  respective  vertical  scale  units  on  the 
right  in  the  curve  chart  directly  opposite  and  at 
the  end  of  the  same  horizontal  line  as  those  on  the 
left.? 

If  the  curve  chart  contains  a  zero  or  100  per 
cent  line,  has  it  been  made  wider  or  heavier  than 
the  other  horizontal  lines.?  If  the  zero  line  is 
not  shown,  does  the  bottom  or  base  line  clearly 
indicate  that  the  vertical  scale  does  not  begin 
with  zero? 


Features  of  a  Complete  Chart        51 

If  it  will  aid  in  the  easy  reading  of  the  curve  see 
that  the  horizontal  scale  figures  are  duplicated  at 
the  base  line. 

In  most  curve  charts  it  is  best  to  have  the 
vertical  scale  figures  on  the  right  as  well  as  on 
the  left  vertical  scale  line.  If  only  one  set  of 
scale  figures  are  used,  however,  these  should  be 
alongside  the  first  or  left  vertical  line. 

Do  not  make  use  of  the  first  and  last  vertical 
lines  of  a  ciu-ve  chart  as  the  neat  lines  of  the  frame. 
They  should  be  reserved  strictly  for  the  vertical 
scale  units  and  should  be  no  heavier  or  wider  than 
the  interior  vertical  lines. 

Do  not  forget  that  it  is  the  independent  variable 
that  takes  the  horizontal  scale,  especially  in 
curve  charts  involving  periods  of  time. 

Follow  each  curve  from  its  beginning  on  the 
left  to  its  termination  on  the  right  to  see  that  it  is 
continuously  correct — that  there  is  no  "break" 
in  it.  See  to  it  also  that  the  curve  is  a  slightly 
heavier  line  than  the  vertical  and  horizontal 
lines. 


QUESTIONS   FOR  SELF-EXAMINATION 

1.  Describe  in  general  terms  the  most  important  char- 
acteristics of  a  curve  chart. 

2.  What  is  the  statistical  table?  What  is  its  relation  to 
the  curve? 

3.  What  is  the  position  of  the  table  on  the  chart?  What 
are  its  general  features?    What  is  meant  by  "boxing?" 

4.  What  is  the  internal  make-up  of  a  table?  What  is  a 
column  heading?    What  is  meant  by  spacing? 

5.  What  is  the  guiding  rule  in  table  construction? 

6.  What  features  of  the  chart  affect  the  form  of  the 
table  and  its  position  on  the  framework? 

7.  What  is  meant  by  duplicating  the  scale  units?  How 
is  this  done?  What  are  the  advantages? 

8.  What  is  the  position  for  the  horizontal  scale?  Give 
reasons  supporting  your  statement. 

9.  What  is  the  function  of  the  word  designation  of  the 
vertical  scale? 

10.  What  is  the  title?  What  is  its  location?  Describe 
the  principles  underlying  the  selection  of  words  for  the 
title. 

11.  What  is  an  asterisk?     What  are  its  uses  in  chartog- 
' raphy? 

12.  What  service  do  foot-notes  perform?  Where  are 
they  located  on  the  chart?  What  do  they  usually  comprise? 

13.  What  are  neat  lines?  What  is  their  position  on  a 
chart? 


62 


LESSON  V 
The  Bar  Chart 

Maldng  Bars  from  a  Curve — MaJcing  a  Curve 
from  Bars — Advantages  of  the  Horizontal  Bar 
— Reversing  the  Scales — Width  of  the  Bar — 
Separation  of  the  Bars — Location  of  the  Table 
— The  Bar  and  the  Curve. 

Emphasis  thus  far  has  been  i)laced  on  the  curve 
as  the  method  of  expression  offered  by  the  art  of 
chartography.  But  tliere  is  also  the  bar.  Many 
of  the  principles  of  construction  already  explained 
in  describing  the  curve  apply  with  equal  force 
to  the  bar  chart.  In  fact,  there  are  many  points 
of  similarity  between  these  two  different  kinds  of 
charts. 

MAKING  BARS  FROM  A  CURVE 

This  the  student  will  be  able  to  realize  clearly 
by  taking  a  curve  chart  and  drawing  vertical 
bars  from  its  base  line  to  the  j)oints  of  the  curve. 
This  has  been  done  in  the  chart  on  page  54.  It 
is  merely  the  result  of  taking  the  curve  chart  on 
page  38  (I^esson  IV)  and  with  as  few  changes  as 
possible  transforming  it  into  a  bar  chart. 

In  order  to  secure  a  bar  for  each  of  the  seven 
years  it  is  necessary  to  add  another  vertical  line 

53 


54 


Chartography  in  Ten  Lessons 


to  the  right  of  the  one  for  the  year  1919  and 
extend  to  it  the  top  and  bottom  horizontal  lines. 
The  horizontal  scale  unit  for  each  year  is  moved 
to  the  right  from  its  former  position  at  the  top 


60 

1913 

1914 

1915 

1916 

1917 

|9I8    1919 

55 
60 
45 

40 

35 
30 

t)5 

40 
35 
30 

, 

?■! 

IHH^^^I^^^i 

pn 

1913 

1914 

1915 

1916 

1917 

1918    1919 

of  a  vertical  line  so  as  to  occupy  space  between 
the  vertical  lines  and  to  be  above  the  top  of  the 
bar.  No  change  is  made  either  in  the  unit  of 
measurement  of  the  vertical  scale  or  in  its  location. 


The  Bar  Chart  55 

making  a  curve  from  bars 

This  procedure  enables  the  many  points  of 
similarity  between  the  curve  and  the  bar  chart 
to  be  quickly  recognized.  This  similarity  will 
all  the  more  be  indelibly  impressed  upon  the 
mind  of  the  student  if  he  will  take  the  vertical 
bar  chart  on  page  54  and  di-aw  a  continuous 
curve  from  left  to  right  touching  the  tops  of  all 
the  bars.  Then  if  he  will  cut  out  a  piece  of  blank 
paper  so  that  its  upper  edge  conforms  roughly 
to  the  curve  he  has  drawn  he  will  find,  by  placing 
this  on  the  bars,  that  the  latter  are  hidden  from 
view  and  that  the  curve  remaining  in  sight  ex- 
presses just  as  clearly  the  tendency  shown  by  the 
bars.  In  other  words,  his  cut  piece  of  blank  paper 
has  simply  restored  tlie  original  curve  chart  on 
page  38  (Lesson  IV). 

This  procedure  also  emphasizes  strikingly  the 
essential  difference  between  tliese  two  kinds  of 
charts.  This  difference  lies  primarily  in  the  fact 
that  the  horizontal  scale  of  a  curve  registers  j)oints 
on  lines  while  tlie  horizontal  scale  of  a  vertical 
bar  chart  registers  space  between  points  on  lines. 

liut  in  cliarigirig  tlie  curve  to  tlie  bar  we  have 
not  secured  a  good  bar  chart.  In  the  first  place 
the  bars  are  entirely  too  wide  to  represent  such 
small  amf)unts  as  fciits.  In  the  second  j)lace  the 
bars  take  ui>  entirely  too  much  .sj)ace — the  same 


56  Chartography  in  Ten  Lessons 

ends  can  be  accomplished  by  the  use  of  a  narrower 
bar.  In  the  third  place  the  result  is  a  vertical 
bar,  that  is,  a  bar  standing  upright  on  its  end. 
A  horizontal  bar,  that  is  one  lying  on  its  side  and 
extending  from  left  to  right,  is  preferable. 

ADVANTAGES  OF  THE  HORIZONTAL  BAR 

This  preference  is  based  on  an  experience  of 
years  in  meeting  the  every-day  problems  of 
chartography.  It  convinces  the  writer  of  the 
greater  utility  of  the  horizontal  bar.  Quite 
probably  there  are  occasions  when  it  is  advisable 
to  have  recourse  to  the  vertical  bar,  but  at  the 
same  time  where  there  is  a  choice  between  the 
two  the  horizontal  bar  will  be  found  to  be  more 
advantageous.  It  gives  greater  opportunity  for 
the  display  of  letters  and  figures  where  the  limita- 
tions of  space  or  other  considerations  require  that 
these  be  placed  on  the  bars  themselves.  In 
such  instances,  in  order  easily  to  read  the  words 
or  figures  on  vertical  bars  the  chart  usually  has 
to  be  turned  half  way  round  to  the  right,  whereas 
if  the  bars  are  horizontal  the  figures  and  letters 
read  in  the  natural  direction.  In  brief,  with  the 
vertical  bar  the  chartographer  will  encounter  more 
difficulties  than  with  the  horizontal  bar  in  the 
placing  of  his  table,  figures,  and  letters.  The 
ability  to  select  advisedly  in  those  cases  where  it 


The'VBar'^Chart  57 

might  be  advantageous  to  employ  the  vertical 
bar  will  come  to  the  student  AA'ith  practice  and 
experience.  It  is  recommended  that  in  the  mean- 
time he  confine  himself  to  the  practice  of  the 
horizontal  bar. 

Such  a  bar  chart  is  presented  on  the  following 
page.  It  will  be  observed,  from  a  comparison 
of  its  statistical  table  with  that  of  the  curve  chart 
on  page  38  (Lesson  IV),  that  it  is  constructed 
from  the  same  set  of  figures. 

REVERSING  THE  SCALES 

The  horizontal  bar  has  necessitated  a  reversal 
in  the  location  of  the  scales  in  comparison  with 
those  of  the  curve.  Instead  of  the  independent 
variable — the  years — occupying  the  horizontal 
scale  position  it  takes  that  of  the  vertical  scale, 
and  the  dependent  variable — the  prices  of  bacon 
— becomes  in  turn  the  horizontal  scale.  This 
jjcrmits  of  the  measurement  of  the  movement  of 
the  bars  from  left  to  right  and  not  from  the  bottom 
up,  as  with  the  vertical  bar.  Otherwise  we  could 
not  secure  the  advantages  of  the  horizontal  bar. 

In  a  horizontal  l)ar  chart  the  figures  of  the 
vertical  scale,  quite  frequently  comprising  periods 
of  time,  are  located  directly  to  the  left  of  the 
beginning  of  the  bars,  the  figures  for  each  year 
being  centered  adjacent  to  their  respective  bar. 


58 


Chartography  in  Ten  Lessons 


15 

II 


The  Bar  Chart  59 

The  last  digit  of  the  luiniber  should  not  be  per- 
mitted to  crowd  the  end  of  the  bar  too  closely. 

WIDTH    OF   THE    BAR 

It  will  be  noted  that  the  bars  are  narrower 
in  the  chart  on  page  58  than  in  the  one  on  page 
54.  This  feature  of  the  bar  is  important.  Just 
how  narrow  or  liow  wide  or  deep  the  bar  should  be 
will  depend  upon  a  number  of  factors,  such  as 
the  nature  of  the  particular  statistical  problem, 
the  arbitrary  limitations  of  space,  and  so  on.  No 
definite  rule  can  be  given  excejit  that  all  the  bars  of 
a  chart  must  be  of  uniform  width,  they  should  be 
sufficiently  wide  to  be  easilj'  seen,  and  they  should 
convey  an  imi)rcssion  of  the  volume  or  quantity 
represented.  For  instance,  a  bar  re})resenting 
billions  should  be  wider  than  one  representing 
millions;  the  latter  wider  than  one  representing 
liiindreds  of  thousands;  and  the  latter  of  greater 
width  than  one  representing  thousands,  and  so  on. 
Wide  bars  are  preferable  to  too  narrow  ones. 

In  })eginning  to  draw  the  bars  the  student 
should  indicate  on  the  sheet  by  liglit  lead  pencil 
lines  instead  of  dots  the  widtli  and  length  of  each 
bar,  the  former  being  arbitrarily  determined  by 
the  number  of  l)ars  that  is  to  go  in  the  available 
space  and  the  latter  by  the  quantity  or  volume 
each  bar  represents  as  determined  by  the  statis- 


60         Chartography  in  Ten  Lessons 

tics  and  the  scale  unit.  It  is  first  advisable  to 
determine  from  the  statistics  and  the  horizontal 
scale  unit  the  length  of  the  shortest  and  the 
longest  bar.  All  the  other  bars  fall  within  the 
limits  these  two  set.  Begin  plotting  the  chart 
with  the  bar  for  the  earliest  year  at  the  top  and 
just  beneath  the  horizontal  scale  line,  outlining 
the  bars  downward  as  the  years  determine.  These 
skeleton  bars  should  then  be  filled  in  black  by 
rotating  the  pencil  point  within  the  outlines. 

SEPARATION   OF   THE   BARS 

Between  each  bar  representing  the  statistical 
element  of  the  vertical  scale  there  should  be  a 
separation  sufficient  to  distinguish  it  from  the 
preceding  and  following  bar.  In  the  chart  on 
page  58  this  has  been  done  by  leaving  in  the 
original  drawing  a  space  equal  to  one-tenth  of  an 
inch.  Usually  this  is  too  much  spacing.  Besides, 
it  requires  a  greater  amount  of  painstaking  labor 
than  should  ordinarily  be  given  to  a  bar  chart. 
How  this  labor  can  be  eliminated  the  student  will 
be  informed  in  a  succeeding  Lesson. 

The  bar  chart  on  page  58  shows  the  vertical 
lines  extending  from  the  points  of  the  scale 
units  on  the  top  horizontal  line  to  the  base  hori- 
zontal line  except  where  the  bars  and  the  statis- 
tical table  intervene.    These  extend  downward 


The  Bar  Chart  61 

the  units  of  measurement  of  the  horizontal  scale 
to  each  of  the  seven  bars  at  the  various  points  of 
contact  of  the  vertical  lines  with  the  bars.  Ordi- 
narily these  vertical  lines  should  not  be  extended 
between  the  bars  but  to  the  first  bar  only  that 
interferes  with  their  further  extension.  These 
lines  are  permitted  to  be  seen  on  this  chart  merely 
to  inform  the  student  as  to  the  purpose  of  the 
vertical  lines  in  a  bar  chart.  All  sections  of  verti- 
cal lines  that  have  been  drawn  within  the  bars 
should  be  pencilled  out  of  observation  as  the  body 
of  the  bar  is  pencilled  in. 

LOCATION    OF   THE   TABLE 

The  location  of  tlie  statistical  table  in  the  upper 
right  hand  corner  is  that  which  will  usually  be 
found  best  adapted  for  this  use.  This  is  true  be- 
cause this  position,  as  a  general  thing,  is  opposite 
the  shortest  bars  and  thus  has  the  largest  area  of 
unoccupied  space.  The  lower  right  hand  corner 
is  frequently  taken  up  witli  the  extejision  of  the 
longest  bars  rcjjrescnting  the  largest  numbers 
to  be  charted,  and  the  upper  and  lower  left  hand 
corners  always  contain  the  begimii?ig  of  tlic  bars. 

In  cases  where  the  extensions  of  the  bars  from 
the  earliest  to  the  latest  years  show  a  decrease 
instead  of  an  inrrease,  tlie  statistical  table  should 
be  located  in  the  lower  right  hand  corner.    Tlie 


62  Chartography  in  Ten  Lessons 

table  should  be  "boxed,"  that  is,  enclosed  in  a 
light  frame  composed  of  two  vertical  and  two 
horizontal  lines  connecting  at  their  ends  and  form- 
ing right  angles. 

Separating  the  numbers  from  their  table  and 
placing  them  on  the  individual  bars  adjacent  to  the 
figures  of  the  years  will  sometimes  be  found  advan- 
tageous. 

THE   BAR   AND   THE    CURVE 

As  between  the  bar  and  the  curve  chart  the 
latter  will  be  found  to  be  much  more  useful  as 
well  as  more  adaptable  to  a  larger  number  of  statis- 
tical tables  or  problems.  It  is  true  that  in  many 
instances  either  may  be  employed  with  equally 
successful  results.  The  bar  chart,  however,  is 
the  most  common  at  the  present  time  not  only 
because  it  is  the  simplest  to  construct  but  also 
to  interpret.  Its  advantage  lies  in  its  simplicity — 
the  amount  or  quantity  or  statistical  element  is 
simply  represented  by  the  length  of  the  bar.  This 
gives  only  one  dimension  to  be  read  and  in  conse- 
quence there  is  little  ground  for  misinterpreta- 
tion. As  a  general  statement  the  bar  method 
should  be  used  where  the  numbers  represent  large 
volumes  or  quantities. 

At  the  same  time  there  are  special  problems  in 
chartography  which  the  curve  chart  alone  will 


The  Bar  Chart  63 

solve  to  the  best  advantage.  Just  what  are  the 
particular  characteristics  of  these  problems  the 
student  will  learn  by  experience.  The  kind  of 
chart  that  will  best  bring  out  the  true  significance 
of  a  statistical  table  is  the  one  to  select.  It  can  be 
said  generally  that  with  statistical  tables  having 
numbers  representing  very  large  amounts,  such 
as  billions  and  millions,  the  bar  chart  is  preferable. 
Conversely,  where  the  numbers  represent  small 
amounts,  such  as  hundreds  and  tens,  the  curve 
chart  is  usually  the  best.  One  reason  for  this  is  that 
the  bar  conveys  the  idea  of  volume  to  a  greater  de- 
gree than  does  the  curve. 

The  difference  between  these  two  kinds  of  charts 
is  strikingly  presented  by  Brinton  in  his  Graphic 
Methods  for  Presenting  Facts.  He  first  com- 
pares bars  representing  years  or  other  intervals  of 
time  with  progress  photographs.  Though  the  bars 
and  progress  photograi)hs  are  valuable,  he  says, 
they  give  information  only  in  spots.  Then  he  says: 

"A  moving-picture  machine  shows  pictures  so 
rapidly  tiiat  the  pictures  blend  into  a  continuous 
narrative  in  the  eye  and  the  brain  of  the  observer. 
What  the  moving-picture  is  to  separate  progress 
photographs,  the  curve  is  to  detached  bars  repre- 
senting time.  In  just  so  much  as  the  moving-pic- 
ture is  superior  to  separate  pictures  shown  by 
lantern  slides,  in  just  that  much  is  a  curve  superior 


64  Chartography  in  Ten  Lessons 

to  a  series  of  horizontal  or  vertical  bars  for  the 
same  data.  Unless  a  person  knows  thoroughly 
how  to  read  and  how  to  plot  curves  he  cannot 
hope  to  understand  the  graphic  presentation  of 
facts." 

Brinton  also  says:  "A  curve  permits  of  finer  in- 
terpretation than  any  other  known  method  of 
presenting  figures  for  analysis — it  gives  informa- 
tion which  many  persons  might  not  fully  grasp  if 
only  a  column  of  figures  were  used."  And  again 
the  same  author  says:  "One  of  the  chief  advan- 
tages of  the  curve  method  of  presenting  informa- 
tion is  that  a  curve  forces  one  to  think." 

It  will  be  found  that  plotting  the  curve  is  sim- 
pler than  plotting  the  bar.  It  also  consumes  less 
time.  Many  chartographers  prefer  the  curve  to 
the  bar  method  of  presenting  statistics  because 
it  not  only  brings  out  the  fluctuations  from  year 
to  year  more  clearly  to  the  eye  but  also  enables 
the  reader  to  grasp  more  readily  the  tendency 
shown.  The  curve  is  gradually  supplanting  the 
bar  in  popular  usage  because  of  its  greater  clear- 
ness, and  this  tendency  is  likely  to  grow  stronger 
as  its  advantages  over  the  bar  are  more  generally 
recognized. 

QUESTION  FOR  SELF-EXAMINATION 

1.  Describe  the  similarities  and  differences  of  the  curve 
and  bar  chart. 


LESSON  VI 

The  Tools  of  the  Chartographer 

Cross  Section  Paper — The  Lead  Pencil — The 
Kind  of  Ink — The  Ruling  Pen — Correct  Posi- 
tion for  Holding  Pen — Pen  Points — The  Draw- 
ing Board — The  T -Square — The  Triangle — 
The  E?igi?ieer's  Scale — The  Dividers — The 
Essential  Tools. 

If  the  beginner  has  profited  to  the  full  extent 
from  a  careful  and  painstaking  study  of  the  pre- 
ceding Lessons  he  is  now  qualified  to  drop  the 
blank  sheet  of  ordinary  paper,  the  lead  pencil, 
and  the  common  ruler  and  take  up  the  real 
materials  and  tools  of  the  chartographer.  The 
proper  use  of  these  materials  and  tools  will 
measurably  facilitate  and  make  less  difficult 
the  mechanical  work  of  chart  making  and  will 
also  result  in  inucli  better  workmanship.  It 
permits  of  the  chart  becoming  permanently 
valuable  as  well  as  of  its  reproduction  in  any 
number  desired. 

CROSS    SECTION    PAPER 

The  most  important  of  the  essential  materials 
is  the  cross  scftion  or  coordinate  i)aj)er.  A 
sample  illustration   is  shown    on    the    following 

05 


rr 


J 


icx 


-+ 


Tools  of  the  Chartographer  67 

page.  This  section  paper  comprises  minute 
squares  formed  by  horizontal  and  vertical  lines. 
On  the  most  commonly  used  section  paper  each 
minute  square  measures  one-tenth  of  an  inch. 
One  hundred  of  these  squares  make  up  a  larger 
square  of  one  inch,  the  border  lines  forming  the 
square  inch  being  slightly  heavier  than  the  other 
horizontal  and  vertical  lines.  Section  paper  can 
also  be  secured  that  has  other  rulings,  such  as 
eight  minute  squares  each  way  or  sixty-four  to 
the  square  inch,  and  six  each  way  or  thirty-six 
to  the  square  inch. 

Cross  section  paper  thus  presents  a  system  of 
squares  whose  lines  permit  the  easy  measurement 
or  determination,  by  means  of  space  or  distance 
on  the  sheet,  of  the  quantity  or  volume  or  what- 
ever element  it  is  the  statistical  table  represents. 
By  combining  squares,  space  units  of  measure- 
ment as  extended  in  both  directions  as  the  par- 
ticular problem  requires  are  readily  determined. 

A  sufficient  quantity  of  section  paper  for  most 
charting  purposes  can  be  obtained  at  almost  any 
first-class  stationery  store.  If  a  large  number  of 
different  fliarts  is  to  i)e  made  tlie  varying  scales 
will  likely  require  different  subdivisions  of  the 
square  inch  and  as  it  requires  too  much  detail 
labor  for  tlic  cliartf)grai)lu'r  liinisclf  to  draw  these 
subdivisions,  it  is  advisable  for  quantity  produe- 


68  Chartography  in  Ten  Lessons 

tion  to  keep  on  hand  a  supply  of  coordinate 
sheets  with  the  different  ruHngs.  Even  then  the 
chartographer  will  not  always  have  paper  with 
the  ruled  spaces  exactly  corresponding  to  his 
requirement,  and  in  such  cases  he  will  have  to  do 
the  ruling  himself. 

In  sheet  sizes  the  section  paper  is  usually  17 
by  22  inches.  These  sheets  can  be  cut  to  meet 
almost  any  ordinary  requirement;  or  two  or 
more  can  be  pasted  together  along  the  edges  to 
meet  the  demand  for  a  larger  surface  than  that 
commonly  required.  Built-up  sheets  of  paper  can 
also  )e  formed  from  remnants  by  pasting.  If  a 
larger  section-ruled  surface  than  17  by  22  is 
frequently  required  it  will  be  advantageous  to 
purchase  the  coordinate  paper  in  rolls,  in  which 
form  it  is  also  prepared  commercially. 

The  section  paper  used  should  be  of  the  best 
quality.  There  are  cheap  grades  on  the  market 
but  these  do  not  take  the  ink  satisfactorily  and 
have  other  defects,  so  that  in  the  long  run  it  pays 
to  purchase  the  better  grade  at  little  higher 
prices.  Of  course,  a  higher  price  does  not  neces- 
sarily mean  a  better  grade,  but  it  usually  does. 

The  section  paper  best  adapted  to  ordinary 
chart  work  has  the  horizontal  and  vertical  lines 
ruled  in  blue  ink.  On  some  section  paper  these 
lines  are  in  green  or  purple  but  these  colors  are 


Tools  of  the  Chartographer  69 

not  so  desirable,  as  they  are  likely  to  reproduce 
lines  on  the  photographed  chart  that  should  not 
be  shown.  Paper  with  a  soft  surface  should 
also  be  avoided  as  it  will  not  take  the  ink  properly, 
and  from  now  on  we  are  to  make  all  our  charts 
with  pen  and  ink  instead  of  pencil. 

THE   LEAD    PENCIL 

This  does  not  mean  that  the  student  will  have 
no  more  use  for  the  lead  pencil.  In  fact,  he  will 
continue  to  have  constant  need  of  it.  The  lead 
should  )e  neither  too  soft  nor  too  hard — it  should 
not  be  so  soft  as  to  crumble,  or  so  brittle  as  to 
snap  in  two  or  so  hard  as  to  penetrate  or  puncture 
the  drawing  sheet.  The  best  grade  for  general 
use  is  HB. 

Virtually  all  points  of  measurement,  such  as 
the  distances  from  unit  to  unit  of  the  scales  and 
those  of  the  curve  and  each  bar,  should  first  be 
indicated  on  the  section  sheet  by  light  lead  pencil 
marks  or  dots.  This  use  of  the  dots  will  facilitate 
the  drawing  of  the  lines,  curve,  and  l)ars  in  ink. 
The  entire  curve  and  an  outline  of  each  bar  might 
with  advantage  first  be  drawn  in  light  lead  pencil, 
the  ink  being  later  superimposed  after  the  student 
has  satisfied  himself  that  his  pencil  markings 
correctly  represent  the  data.  The  dots  and  other 
lead  pencil  markings  can  be  erased  after  the  ink 


70  Chartography  in  Ten  Lessons 

has  dried.  It  is  much  easier  to  correct  a  mistake 
made  in  lead  pencil  than  one  made  in  ink.  The 
curve  itself  is  made  finally  with  the  draftsman's 
ruling  pen.  The  neat  lines  of  the  frame  are 
drawn  in  ink  after  the  framework  of  the  chart  has 
been  entirely  completed. 

THE    KIND    OF    INK 

The  best  black  ink  for  charting  purposes  is 
Higgins'  American  India.  In  purchasing  ask  the 
dealer  for  waterproof  quality.  This,  when  it 
dries,  is  insoluble  and  will  not  smear  or  spread  in 
case  the  sheet  is  brought  in  contact  with  water, 
as  is  often  the  case  when  the  chart  is  to  be  re- 
produced by  the  blue-printing  process.  Another 
favorable  quality  of  this  ink  is  exhibited  in  the 
process  of  drying  areas  on  charts,  such  as  bars,  as 
it  dries  with  a  flat  or  "dead"  surface.  Such  a 
surface  is  highly  desirable  in  case  the  chart  is  to 
be  reproduced  by  such  photographic  processes 
as  zinc-etching,  photo-lithography,  and  so  on. 
"Chin-chin"  ink,  also  an  India  ink  and  noted 
for  its  opacity,  can  be  used  to  special  advantage 
in  cases  where  the  chart  is  to  be  reproduced  by  the 
blue-printing  process.  While  special  mention  is 
made  of  these  two  inks,  there  are  also  other  India 
inks  on  the  market  equally  as  good  for  ordinary 
charting  purposes.    With  the  smaller  bottles  is 


Tools  of  the  Chartographer  71 

usually  supplied  a  oeveled  quill  inserted  in  the 
cork  which  is  used  in  filling  the  ruling  pen. 

THE   RULING    PEN 

This  ruling  pen  is  an  invaluable  tool  to  the 
chartographer.  It  has  two  blades  or  tines  the 
relation  of  each  to  the  other  being  controlled  by 
an  adjusting  screw.  The  manipulation  of  this 
screw  permits  the  drawing  of  lines  of  varying 
widths.  The  use  of  the  ruling  pen  should  be  con- 
fined to  line  and  curve  work.  Some  pens  have  a 
lever  attachment  which  permits  the  cleaning  of 
the  tines  without  disturbing  the  gauge  at  which 
they  may  be  set.  This  lever  saves  the  time  re- 
quired to  make  the  j^roper  adjustment  again  and 
prevents  the  possibility  of  the  chartographer 
resuming  work  with  a  different  adjustment  of  the 
tines. 

CORRECT   position   FOR   HOLDING   PEN 

The  ruling  })en  should  be  held  in  such  a  position 
as  to  be  in  a  plane  i)erj)endicular  to  the  surface 
of  the  drawing  sheet,  the  tips  of  the  thumb  and 
forefinger  grasping  the  pen  at  tlie  adjusting 
screw.    This  is  illustrated  on  the  following  page. 

Holding  tlie  pen  in  tiiis  way  permits,  when 
necessary,  the  manipulation  of  the  screw  by 
slightly  raising  the  pen  from  contact  with  the 


72 


Chartography  in  Ten  Lessons 


sheet.  In  ruling  lines  or  curves  the  hand  or 
fingers  should  not  touch  the  paper,  nor  should 
the  elbow  rest  on  the  sheet.     The  movement  of 


the  pen  is  not  from  the  hand  but  is  a  free  elbow 
movement  and  is  from  left  to  right  and  from  bot- 
tom to  top  of  the  sheet. 


Tools  of  the  Chartographer  73 

Failure  to  observe  these  instructions  will  result 
in  the  points  of  the  tines  wearing  away  unevenly 
and  the  pen  then  develops  what  is  referred  to  by 
draftsmen  as  a  "shoulder."  This  usually  means 
that  this  particular  pen  must  be  discarded  for 
line  and  curve  work  as  it  is  no  longer  a  "true" 
instrument  or  tool.  These  old  pens  can  be  used  to 
advantage,  however,  in  filling  in  bars,  they  being 
operated  in  such  cases  somewhat  as  one  would  a 
small  brush.  It  is  not  impossible  to  remove  a 
"shoulder"  from  a  ruling  pen.  This  can  be  done 
by  using  a  small  oil-stone  or  razor-hone.  The 
stone  or  hone  can  also  be  used  to  advantage  in 
keeping  the  points  of  the  tines  sharp  and  true. 
In  this  process  of  sharpening  be  careful  to  hold 
the  ruling  pen  against  the  surface  of  the  stone  or 
hone  at  an  angle  of  about  forty-five  degrees, 
grinding  the  points  with  a  gentle  rotary  motion. 
Follow  this  by  rubbing  the  points  of  the  tines  on 
any  glass  surface.  An  examination  of  the 
points  should  then  find  all  "burrs"  or  unevenness 
to  have  been  removed. 

PEN  points 

In  addition  to  the  ruling  pen  and  as  a  substitute 
for  it  in  many  uses,  the  student  will  need  pen 
points  and,  of  course,  a  j)ciihol(ler  or  holders. 
For  fine  line  work  and  small  lettering  Gillett's 


74  Chartography  in  Ten  Lessons 

No.  303  is  recommended.  Esterbrook's  No.  14 
bank  pen  point  is  also  good  for  lettering.  Gillett's 
No.  291  will  also  be  found  satisfactory,  especially 
in  mapping  work. 

The  student  is  no  doubt  familiar  through  per- 
sonal experience  with  the  fact  that  most  pen 
points  when  first  dipped  in  ink  repel  or  throw  off 
the  ink.  This  is  likely  to  result  in  blots  or  spots 
if  it  occurs  on  a  sheet  of  drawing  paper.  To 
obviate  this  it  is  suggested  that  the  pen  point  be 
held  for  a  moment  in  the  flame  of  a  match  before 
being  put  to  use  for  the  first  time. 

THE   DRAWING   BOARD 

The  effective  use  of  the  section  paper,  the  pen- 
cil, the  ruling  pen,  the  pen  points,  and  the  ink 
makes  necessary  that  the  student  also  have  a 
drawing  board.  This  is  nearly  always  made  of 
neatly  glued  strips  of  soft  wood,  usually  white 
pine,  with  a  hardwood  ledge  of  an  inch  or  so  on 
each  end.  The  board  can  be  secured  in  varying 
sizes  ranging  from  12  by  17  inches  to  31  by  42 
inches.  Larger  sizes  can  also  be  purchased.  The 
board  rests  unattached  on  the  desk  or  table  and 
can  be  moved  about  freely  with  the  section  paper 
temporarily  attached  to  it  by  means  of  thumb 
tacks.  In  case  the  student  prefers  a  drawing  table, 
this  can  be  had  in  various  makes  and  designs. 


Tools  of  the  Chartographer  75 

the  t-square 

The  drawing  board  or  table  facilitates  greatly 
the  use  of  the  T-Square,  another  tool  of  the  char- 
tographer which  he  will  find  invaluable.  It  is 
so-called  because  of  its  resemblance  to  the  cap- 
ital letter  T.  For  all  purposes  of  accurate  line 
drawing  not  involving  measurement  it  supplants 
the  ordinary  ruler.  A  T-Square  fitted  with  trans- 
parent ruling  edges  is  reconmiended,  as  it  permits 
the  draftsman  to  see  adjacent  portions  of  the 
section  sheet  that  would  be  hidden  if  a  wooden 
straightedge  were  used.  It  fits  in  snugly  and 
along  either  ledge  of  the  board  or  table  accurately 
by  reason  of  the  head  piece  of  the  T-Square  ex- 
tending beneath  the  blade  with  its  ruling  edges. 
This  permits  of  a  true  base  line  as  well  as  other 
horizontal  lines.  Upon  this  base  line,  with  theT- 
Square  in  position,  true  vertical  lines  are  erected 
by  means  of  the  Triangle. 

THE  TRIANGLE 

The  use  of  the  Triangle  is  largely  confined  to 
making  vertical  and  horizontal  lines.  Do  not 
attempt  to  draw  these  lines  with  the  ordinary 
ruler  if  any  degree  of  accuracy  is  desired  as  such 
an  attempt  will  most  likely  result  in  inaccuracy. 
Accuracy,  it  should  be  remembered,  is  one  of  the 
cardinal  principles  of  good  chartography. 


76  Chartography  in  Ten  Lessons 


J 

o                                                  o 

E^ 

o                                                    o 

Fie.  1 


FI6.  2 


Tools  of  the  Chartographer  77 

The  illustration  on  the  preceding  page  shows 
some  of  the  uses  to  which  the  Triangle  is  put  when 
operated  in  connection  with  its  running-mate,  the 
T-Square.  Triangles  are  obtainable  in  numerous 
sizes  and  angles,  the  standard  angles  being  45 
degrees  and  30  by  60,  the  latter  commonly  called 
"Thirty"  by  draftsmen. 

THE     engineer's     SCALE 

Important  uses  will  also  be  found  in  chart 
making  for  the  engineer's  rule  or  scale.  It  is  an 
equilateral  triangle  in  shape,  that  is,  all  its  sides 
are  equal;  it  is  usually  made  of  hardwood,  12 
inches  in  length  (although  different  lengths  are 
procurable),  and  has  three  edges  each  with  two 
measuring  surfaces.  These  six  surfaces  are  laid 
of!  into  multiples  of  10,  with  10,  20,  30,  40,  50,  and 
60  units  to  the  inch,  and  in  consequence  they 
provide  measurements  of  almost  any  fraction  of 
an  inch  that  can  be  quickly  aj)plied  to  varying 
scale  units  of  less  than  an  inch.  The  engineer's 
.scale  is  admirably  adapted  to  linear  measure- 
ments, that  is,  to  measurements  pertaining  to  or 
of  the  nature  of  a  line  or  in  one  direction. 

The  engineer's  triangular  scale  is  not  to  he 
confused  with  the  architect's  triangular  scale,  the 
latter  having  the  inch  divided  into  units  of  fourths, 
eighths,   sixteenths,    thirty-seconds,    and   so   on, 


78  Chartography  in  Ten  Lessons 

and  which  is  of  little  use  to  the  chartographer. 
The  student  is  cautioned  against  making  use  of 
the  engineer's  rule  for  ordinary  ruling  purposes, 
as  this  use  wears  away  the  ruled  edges  and  in 
time  makes  ineligible  the  sub-divisions  of  the 
inch. 

THE  DIVIDERS 

Assistance  in  the  drawing  of  a  chart  is  also 
rendered  by  the  use  of  the  compass  or  dividers. 
It  consists  of  a  handle  from  which  extends  two 
prongs  each  having  a  sharp  point.  In  the  handle 
is  a  joint,  either  a  pivot  or  tongue,  which  permits 
adjustments  between  the  two  points  up  to  several 
inches.  This  enables  the  draftsman  to  "step- 
off"  or  gauge  accurately  any  measurements  on 
lines  or  charts  that  are  to  be  transferred  to  other 
lines  or  charts.  Greater  accuracy  will  be  se- 
cured from  the  use  of  the  dividers  than  from  that 
of  the  ordinary  ruler  for  this  purpose. 

Every  draftsman  has  use  for  kneaded  rubber, 
art  gum,  and  the  "ruby"  or  red  rubber  eraser  for 
erasure  purposes.  A  hard  rubber  or  gritty  eraser, 
such  as  the  ordinary  typewriter  eraser,  should 
not  be  used.  A  supply  of  pins,  clips,  thumb 
tacks,  and  the  like  will  also  come  in  handy. 

THE  ESSENTIAL  TOOLS 

The  following  summarizes  the  more  important 
tools  needed  in  chartography: 


Tools  of  the  Chartographer  79 

One  drawing  pencil  HB. 

One  ruling  pen. 

Six  Gillett's  No.  303  and  six  Easterbrook's 
No.  14  pen  points. 

One  bow  or  compass  pen  with  interchangeable 
pen  and  pencil  points  and  extension  bar. 

One  bottle  Higgin's  waterproof  black  drawing 
ink. 

One  drawing  board  or  table. 

One  T-Square. 

One  six-inch  celluloid  45  degree  triangle. 

One  twelve-inch  engineer's  triangular  rule. 

One  dividers. 

These  tools  can  each  be  bought  separately  but 
a  material  saving  is  made  by  purchasing  a  com- 
plete set  of  drawing  instruments  at  the  outset. 
The  price  naturally  varies  according  to  the  quality 
but  an  expensive  set  is  not  necessary  for  good 
work.  The  outfit  of  the  chartographer  may  be 
simple  or  elaborate  according  to  individual  taste. 
A  few  well  selected  instruments  of  standard  make 
is  recommended  at  first.  Where  tiie  beginner 
confines  himself  to  a  limited  number  of  tools  he 
becomes  familiar  with  the  "feel"  and  balance 
of  each  instrument  and,  as  a  result,  soon  learns 
to  handle  it  with  confidence  and  skill.  This 
applies  especially  to  the  drafting  or  ruling  pen. 


QUESTIONS  FOR  SELF-EXAMINATION 

1.  What  is  cross  section  or  coordinate  paper?  What  ser- 
vice does  it  perform  in  chartography? 

2.  What  is  the  function  of  the  lead  pencil  in  chart 
making? 

3.  What  is  the  ruling  pen?  Describe  the  correct  posi- 
tion for  holding  it.  What  is  a  "shoulder"  and  what  causes 
it?  How  can  it  be  prevented? 

4.  Describe  the  drawing  board  and  its  uses. 

5.  What  is  the  T-Square  and  what  are  its  uses?  The 
Triangle? 

6.  What  is  the  engineer's  scale?  How  and  for  what 
purposes  is  it  employed? 

7.  Describe  the  dividers  and  its  uses. 

8.  What  are  the  essential  tools  in  chartography? 


80 


LESSON  VII 

Accuracy  in  Chartography 

The  Use  of  the  Typewriter — Drawing  Letters 
for  the  Title — Exaggerating  the  Curve — Effects 
of  Exaggerating  the  Curve — Advantages  of 
Extra  Squares. 

In  placing  on  the  chart  the  figures  of  the  scale 
lines,  the  statistical  table,  the  foot-notes,  and 
other  figures  and  letters  the  use  of  the  typewriter 
enables  the  chartographer  to  meet  many  of  the 
exactions  encountered  in  the  practice  of  his  art. 
This  is  especially  true  when  a  large  number  of 
different  charts  has  to  be  made  for  reproduction 
in  quantities  by  means  of  one  of  the  photographic 
processes. 

THE  USE  OF  THE  TYPEWRITER 

If  a  long-carriage  machine  is  not  available  and 
if  the  coordinate  sheet  is  too  large  for  the  ordinary 
typewriter  the  sheet  can  be  cut  in  two  and  after- 
wards pasted  together.  This  makes  necessary 
the  exercise  of  care  in  handling  the  sheet  after- 
wards or  else  the  typewritten  figures  will  "rub." 
This  work  on  the  typewriter  should  be  done  after 
the  lines  aiul  curve  or  bars  are  completed. 

Another  practice  that  has  many  advantages  is 

81 


82  Chartography  in  Ten  Lessons 

first  to  typewrite  the  numbers  and  words  on 
separate  slips  of  paper  and  then  paste  these 
securely  in  their  proper  places  on  the  section  sheet. 
This  plan  should  be  followed  if  the  chart  is  to  be 
reproduced.  It  enables  corrections  to  be  made 
more  easily  and  does  not  wrinkle  or  otherwise 
damage  the  sheet.  If  the  chart  is  not  to  be 
reproduced,  the  letters  and  figures  should  be 
written  according  to  the  first  plan,  that  is  directly 
on  the  coordinate  sheet  itself. 

Typewriting  the  table  directly  on  the  chart  or 
on  a  separate  slip  of  paper  and  later  pasting  this 
on  the  sheet,  requires  considerable  painstaking 
care.  The  typed  figures  and  letters  must  be 
clean,  decimal  points  separating  the  digits  must 
be  in  column  order  equally  exact  with  the  fig  ires 
themselves,  units  of  tens  or  hundreds  and  so  on 
must  be  under  each  other,  and  all  in  straight 
columns  with  headings  appropriately  placed  at 
the  top  of  each.  In  pasting  the  slip  on  the  sheet 
exactness  is  required  so  as  to  avoid  the  appearance 
of  "skewness."  Corrections  can  more  easily  be 
made  with  the  figures  and  letters  on  the  slip 
than  with  them  directly  typed  on  the  coordinate 
sheet. 

In  the  employment  of  the  typewriter  for  plac- 
ing words  and  numbers  on  a  chart  that  is  to  be 
reproduced  by  a  photographic  process,  care  must 


Accuracy  in  Chartography  83 

be  exercised  in  seeing  to  it  that  the  ink  of  the  tj'pe- 
writer  ribbon  is  of  a  quality  that  will  reproduce. 
I  know  of  the  experience  of  a  fellow  chartographer 
who  had  in  progress  a  rush  contract  for  several 
hundred  different  charts  on  each  of  which  was 
to  be  reproduced  a  statistical  table.  He  failed 
to  have  proper  attention  given  to  overseeing  the 
typing  of  these  tables,  with  the  result  that  not 
one  would  reproduce  because  the  right  kind  of  ink 
was  not  used,  In  itself  the  kind  of  ink  may  be  a 
small  matter  but  the  consequence  of  not  using  the 
right  kind  is  likely  to  prove  serious  and  costly. 

DRAWING    LETTERS    FOR    THE    TITLE 

Virtually  all  the  figures  and  letters  required  on 
a  chart  can  be  placed  in  their  proper  positions 
by  means  of  the  typewriter  with  the  exception  of 
the  title  letters.  These  latter  are  usually  larger 
thaji  those  of  the  typeA\riter,  although  even  for 
the  title  the  capitals  of  the  tj7>ewriter  can  some- 
times be  made  to  serve  the  requirements.  As  a 
general  thing,  however,  the  use  of  the  typewriter 
for  the  title  letters  is  inadvisable. 

It  is  this  lettering  for  the  title  that  is  among 
the  exactions  of  chartograj)liy  with  which  the 
beginner  is  likely  to  have  some  difliculty.  He 
niu.st  learn  h(>^\  to  make  the  kin<l  of  letters 
required.     This   is  not  so  difficult    as  might  at 


84 


Chartography  in  Ten  Lessons 


first  appear;  in  fact  it  is  qujte  simple,  ahd  by  a 
little  practice  the  student  can  soon  become  pro- 
ficient in  this  phase  of  the  work. 

In  making  these  larger  letters  the  minute 
squares  of  the  coordinate  sheet  are  of  material 
assistance.  After  determining  upon  the  size  of 
the  letter  required,  the  horizontal  and  vertical 
lines  of  each  letter  are  drawn  by  the  ruling  pen 
and  with  the  aid  of  the  minute  squares.  The 
curved  corners  are  first  left  blank,  as  illustrated 
in  the  following : 


mms 


Then  the  curved  corners  are  filled  in  with  a  free 
hand  pen. 

For  the  guidance  of  the  beginner  in  chartog- 
raphy the  letters  of  the  alphabet  are  reproduced 
on  the  opposite  page  as  samples  of  plain  and 
easily  made  letters  based  upon  the  above  instruc- 
tions as  to  how  they  are  to  be  drawn.  No 
attempt  is  made  to  present  other  than  a  simple 
utility  alphabet,  all  the  letters  with  the  exception 


86         Chabtography  in  Ten  Lessons 

of  I,  M,  and  W  being  approximately  of  the 
same  width.  Illustration  is  also  given  as  to  the 
drawing  of  large  figures. 

EXAGGERATING  THE  CURVE 

The  beginner  in  chartograpliy,  however,  should 
know  how  to  make  letters  and  should  not  neglect 
to  become  proficient  in  this  direction.  Practice 
in  lettering  teaches  painstaking  accuracy,  and 
this  is  demanded  of  the  good  chartographer. 
In  chart  making  he  will  have  many  opportunities 
for  acquiring  this  personal  asset. 

Especially  is  this  true  in  the  process  of  determin- 
ing and  plotting  the  scales  for  the  curve  chart. 
He  must  be  certain  that  his  vertical  scale  does 
not  permit  of  the  exaggeration  of  the  move^ient 
of  the  curve.  This  exaggeration  easily  results 
in  not  allowing  for  the  vertical  scale  the  same 
amount  of  space  per  each  scale  unit  as  for  the 
horizontal  scale,  and  vice  versa.  In  other  words 
the  movement  of  the  curve  can  be  exaggerated 
either  vertically  or  horizontally. 

"The  scales  of  any  curve  chart  should  be  so 
selected,"  says  Brinton,  in  Graphic  Methods  for 
Presenting  Facts,  "that  the  chart  will  not  be 
exaggerated  in  either  the  horizontal  or  the  ver- 
tical direction.  It  is  possible  to  cause  a  visual 
exaggeration  of  data  by  carelessly  or  intentionally 


Accuracy  in  Chartography  87 

selecting  a  scale  which  unduly  stretches  the  chart 
in  either  the  horizontal  or  the  vertical  direction," 

"The  beginner  in  curve  plotting  and  in  curve 
reading,"  continues  Brinton,  "is  apt  to  be 
somewhat  puzzled  by  the  different  effects  which 
may  be  obtained  by  changing  the  ratio  between 
the  vertical  scale  and  the  horizontal  scale.  It 
is  difficult  to  give  any  general  rules  which  would 
assist  in  overcoming  the  beginner's  confusion. 
Ordinarily  the  best  way  to  get  facility  in  making 
the  proper  choice  of  vertical  and  horizontal 
scales  for  plotting  curves  is  to  take  one  set  of 
data  and  plot  those  data  in  several  different  ways, 
noticing  the  changes  which  the  different  scales 
selected  give  in  the  proportions  of  the  chart. 
Just  as  the  written  or  spoken  English  language 
may  be  used  to  make  gross  exaggerations,  so 
charts  and  especially  curves  may  convey  exag- 
gerations unless  the  person  preparing  the  charts 
uses  as  much  care  as  he  would  onlinarily  use  to 
avoi<l  exaggerations  if  presenting  liis  material 
by  written  or  spoken  words." 

"A  person  reading  charts  must  take  great 
care,"  concludes  Brinton  on  this  })<)int,  "that 
he  does  not  give  too  much  weight  to  the  actual 
appearance  of  the  curve  on  the  page,  instead  of 
basing  his  conclusions  on  the  i)erccntage  increase 
or  decrease  as  judged  from  the  figures  of  the  ver- 


88  Chartography  in  Ten  Lessons 

tical  scale.  The  proper  choice  of  scales  for  curve 
plotting  is  largely  a  matter  of  judgment,  and  the 
judgment  can  be  trained  very  greatly  if  it  is  kept 
in  mind  to  examine  every  curve  chart  which 
comes  to  one's  attention  to  see  whether  the  verti- 
cal and  horizontal  scales  have  been  selected  so  that 
the  chart  gives  a  fair  representation  of  the  facts." 

EFFECTS   OF   EXAGGERATING   THE   CURVE 

The  effects  of  an  exaggeration  of  the  vertical 
scale  can  be  seen  from  a  study  of  the  chart  on  the 
opposite  page.  The  units  of  the  vertical  scale 
are  there  purposely  made  twice  the  distance  apart 
than  are  units  of  the  horizontal  scale.  The  result 
is  an  exaggeration  to  the  eye,  in  the  rise  and  fall 
in  the  movements  of  the  curve  across  the  sheet, 
of  just  twioe  what  these  movements  should  be. 

In  order  that  the  student  may  comprehend 
clearly  for  himself  just  what  this  exaggeration  of 
the  curve  means,  it  is  suggested  that  he  draw  on 
the  chart  on  page  89  in  light  lead  pencil  a  broken 
or  dash  curve  that  conforms  to  a  scale  by  which 
the  distance  between  the  horizontal  lines  is  re- 
duced one-half.  In  other  words,  he  is  to  give  to 
each  horizontal  and  vertical  scale  unit  exactly 
the  same  space. 

Rearranging  the  vertical  scale  units  accordingly 
the  unit  7  falls  on  the  vertical  line  at  a  point  half 


IMMIGRATION   TO   UNITED  STATES   BY  MONTHS,    1918 


TboTiAaMe  of  IXBlffTAnts 
Jaz3.     Feb.      Mar.     Apr.       May      Jun*     July      Aag,    3«pt.    Oct.     lOT.     Oto. 


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Ju.            6,3S« 
r«b.            7,388 
Uu-.            6.510 
Apr.            9,641 
lliiy           IS. 217 
JtUW          14,247 
Jnly            7,780 
toe-             7,862 
sept.          9.997 
Oat.           11,771 
HOT.           8,499 
Dee.         10,748 

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9t«ttatU«  Aj-*  fros  Btu-«ftu  of    l^lgraticn 
0.    3.    0«p*rt««nt    of    Labor 


90         Chartograpiiy  in  Ten  Lessons 

way  between  the  unit  6  and  the  present  7,  and  the 
point  now  marked  by  the  latter  becomes  the 
place  for  the  scale  unit  8.  Proceeding  upward 
in  this  manner  cross  out  with  the  lead  pencil  each 
of  the  old  vertical  scale  units  and  substitute  the 
new  units  according  to  the  revised  plotting.  Re- 
produce in  lead  pencil  this  new  scale  also  alongside 
the  extreme  right  vertical  line.  Connect  these 
new  left  and  right  vertical  scale  points  by  horizon- 
tal lines  in  light  lead  pencil.  Next  draw  the 
curve  from  point  to  point  of  the  vertical  lines  as 
determined  by  the  revised  units. 

It  will  now  be  found  that  this  new  curve  moves 
up  and  down  exactly  one-half  the  distance  of  the 
original  curve.  The  new  curve  starts  at  a 
point  on  the  left  vertical  line  just  above  the  pre- 
sent scale  designation  6  and  ends  at  a  point  on  the 
right  vertical  line  half  way  between  the  present 
scale  units  8  and  9.  These  vertical  scale  units 
represent  thousands  of  immigrants,  as  explained 
in  the  word  designation  just  above  the  horizontal 
scale  line. 

It  is  important  to  remember  in  connection  with 
the  exaggeration  of  the  curve  that  the  arbitrary 
limitations  of  space  imposed  upon  the  chartog- 
rapher  does  not  permit  him  in  every  case  to  choose 
the  scale  that  might  have  been  chosen  if  there 
were  no  factors  to  consider  other  than  the  exact 


Accuracy  in  Chartography  91 

presentation  of  the  statistics.  His  problem  is  to 
present  the  facts  as  clearly  as  possible  within  the 
arbitrary  limitations  of  space  imposed  upon  him. 
Sometimes  he  will  find  himself  in  a  quandary  in 
his  endeavors  to  include  all  the  necessary  data 
without  exaggerating  one  or  the  other  of  the 
scales. 

ADVANTAGES  OF  EXTRA  SQUARES 

Reducing  by  one-half  the  space  allowed  the  ver- 
tical scale  unit  in  the  chart  on  page  89  brings  the 
lowest  and  the  highest  points  of  the  curve  within 
a  space  of  less  than  three  inches,  thus  decreasing 
horizontally  as  compared  with  the  old  curve  the 
size  of  the  area  within  which  the  curve  moves 
without  affecting  its  size  vertically.  Plotted  in 
this  way  results  in  an  awkward  size  for  the  chart. 

This  can  he  overcome  by  providing  at  least  two 
series  of  squares  both  below  the  lowest  and  above 
the  highest  points  recorded  by  the  movement  of 
the  curve.  In  such  cases  the  vertical  and  hori- 
zontal lines  forming  the  squares  are  drawn  just  as 
if  they  were  to  be  used  to  indicate  a  stage  in  the 
movement  of  the  curve.  This  extension  of  the 
area  of  the  sqnares  should  also  be  regulated  so  as 
to  accommodate  the  placing  of  tlio  statistical 
table  without  crowding.  It  will  nearly  always  be 
found  feasible  in  i>lotting  the  vertical  scale  to 


92  Chartography  in  Ten  Lessons 

provide  for  at  least  one  series  of  squares  vertically 
into  which  the  movements  of  the  curve  do  not 
enter.  This  will  be  found  to  be  advantageous  in 
a  number  of  ways.  It  adds  to  clearness  of  expres- 
sion as  well  as  avoids  the  appearance  of  crowding. 
If  the  exaggeration  of  the  scale  in  the  chart  on 
page  89  had  been  in  the  horizontal  instead  of  the 
vertical  measurement,  just  the  opposite  effects  to 
those  noted  would  have  resulted.  It  is  suggested 
that  the  student  draw  a  chart  in  which  he  gives 
twice  the  space  to  the  horizontal  scale  unit  that  he 
gives  to  the  vertical  scale  unit,  using  the  data  in 
the  statistical  table  of  the  chart  on  page  89. 

QUESTIONS  FOR  SELF-EXAMINATION 

1.  Describe  the  various  uses  of  the  typewriter  in  chart- 
ography. 

2.  How  are  large  letters  drawn  by  hand? 

3.  How  is  the  curve  exaggerated?    What  are  some  of  its 
effects?    How  can  these  be  avoided? 

4.  What  are  the  advantages  of  extra  squares? 


LESSON  VIII 
Curve  and  Bar  Designations 

Disadvantages  of  the  Unbroken  Curve — Curve 
Designations — Word  Designations  of  Curves — 
The  Peak-Top  Curve — Determining  the  Scale 
Spacing — Utility  of  the  Curve  Chart — Chartog- 
raphy  Based  on  Comparisons — Bar  Designa- 
tions— Interpreting  the  Bar — Some  Character- 
istics of  a  Good  Bar  Chart — Word  Designation 
of  Scale  Units. 

It  is  plain  that  if  a  number  of  curves  on  the 
same  chart  are  each  drawn  as  an  unbroken  curve 
much  confusion  w  ill  accomjjany  eliorts  to  interpret 
the  tendencies  showTi,  as  most  likely  the  curves 
cross  and  re-cross  each  other.  This  is  illustrated 
in  the  chart  on  the  following  page. 

disadvantages  of  the  unbroken  curve 

Let  the  student  try  to  follow  each  curve  from 
its  beginning  on  the  left  vertical  scale  line  to  its 
termination  on  the  right  vertical  scale  line.  It 
is  hardly  jjossible  that  he  acc(inii)li.shcs  the  task 
successfully  in  every  case  by  ending  on  the  curve 
he  starts  out  upon,  as  indicated  by  the  initial 
abbreviation  of  the  name  of  the  railroad.  Even 
if  he  does  succeed  he  will  have  .spent  a  great  deal 

93 


3 
i   f 


O    4  Vt    U  «    h    • 


«3       ..^S  a^ 
•  «  •  <  ^  • 


Curve  and  Bar  Designatioxs  95 

more  time  than  should  be  required  to  interpret 
such  a  chart  correctly.  Among  the  aims  of 
chartography  is  to  prevent  confusion  and  to  aid 
comprehension  at  a  glance,  and  the  reading  of  a 
chart  should  not  have  placed  in  the  way  obstacles 
like  those  illustrated  on  the  oi)i}Osite  page,  es- 
pecially when  the  obstacles  have  no  reason  or 
even  excuse  for  being.  A  study  of  the  chart 
should  quickly  convince  the  student  of  the  dis- 
advantage of  using  the  same  kind  of  unbroken 
curve  for  two  or  more  statistical  elements  on  the 
same  chart.  Reading  the  chart  in  question  is 
only  slightly  aided  by  placing  at  the  left  and  right 
vertical  scale  lines  the  abbreviations  of  the  names 
of  the  different  railroads  which  the  curves 
represent. 

CURVE  DESIGNATIONS 

Attention  is  thus  called  to  a  practical  condi- 
tion confronting  the  chartographer  which  would 
be  replete  with  difliculties  <lid  he  not  have  re- 
course to  a  simi>le  device  to  overcome  them. 
This  is  the  em7>Ioyment  of  (lifferont  designations 
for  two  and  more  curves. 

In  contrast  with  the  unbroken  or  str.iight  line 
curves  of  the  diart  on  page  94,  those  of  the  chart 
on  page  96  should  be  studied.  The  latter  com- 
pare as  many  as  nine  separate  and  distinct  sta- 


AVERAGE   PRICES'OF   MEAT   PRODUCTS 
UNITED  STATES.     191  3- 1819 


Oraok  Ro*et 


Sirloin  ateti 
Bound  3teak 
Porit  Chops 

Mb  BMst' 
Chuok  RoAflt 
PUta  to«f 


1915  1914  1916  1916  1917  }91»  1919 
16.7   26.7    26.4    2«.l    iS.Z  49.5    i7.2 

26.5  26. B  25.3  }1.2  36.5  44.6  52.9 
26.4  26.4  26.1  27.0  51.7  36.6  43.7 
22.3   23.0   22.3    24.0  26.9    34.5  40.5 

21.6  21.6  19.7  22.6  30.6  36.6  41.4 
20.2  19.3  21.0  23.0  27.6  56.5  39.9 
19.9  20.1  19.7  21.0  25.2  29.3  34.6 
16.2  17.0  16.0  21.2  21.2  25.5  2«.4 
12.2   12.4   12.2   12.6   16.1    19.9   22.6 


CBUOK  lout 


Curve  and  Bar  Designations  97 

tistical  elements,  presenting  two  more  curves 
than  are  in  the  chart  on  page  94,  and  yet  there  is 
not  the  sHghtest  difficulty  or  confusion  in  tracing 
the  nine  curves  from  their  beginning  to  their 
termination.  This  greater  clearness  and  ease  of 
interpretation  is  almost  entirely  due  to  the  fact 
that  a  different  designation  is  given  to  each  curve. 
If  this  had  not  been  done  it  would  l)e  almost  as 
difficult  to  follow  the  curves  in  the  chart  on  page 
9G  as  in  the  chart  on  page  94 — the  curves  of  the 
former  would  also  be  lost,  as  to  the  reading  of 
their  movement,  at  the  points  where  they  cross 
and  re-cross  one  another. 

Quite  frequently  the  student  of  chartography 
will  encounter  the  problem  of  having  many 
curves  to  compare.  While  this  difficulty  is  met 
in  part  by  employing  different  designations  for 
the  curves,  there  will  be  occasions  when  even 
this  method  will  result  in  confusion.  Under  such 
circumstances,  instead  of  attempting  to  draw  all 
the  curves  on  a  single  chart,  it  will  be  found 
advantageous  to  make  two  or  more  charts.  One 
set  of  the  grouj)  of  figures  should  be  selected  as  a 
common  basis  for  the  comi)arisoii  and  the  curve 
representing  this  set  or  statistical  element  in- 
.serted  on  all  the  charts,  this  curve  taking  the 
.same  uribrf)kcii  or  straight  line  designation  on 
each   chart.      It    is   a   mistake   to   i)lace  a   larger 


98         Chartography  in  Ten  Lessons 

number  of  curves  on  one  chart  than  can  be  read 
quickly  and  without  confusion  to  the  eye  in 
tracing  their  movements.  Where  the  curves  lie 
close  together  or  are  constantly  crossing  and  re- 
crossing  each  other,  more  than  five  or  six  are 
likely  to  result  in  this  confusion. 

It  is  in  making  clear  just  such  problems  as 
those  presented  in  the  chart  on  page  96,  where  a 
number  of  different  statistical  elements  must  be 
compared,  that  the  advantage  of  the  curve  method 
over  the  statistical  method  becomes  apparent. 
To  grasp  quickly  and  comprehendingly  the  mean- 
ing of  each  of  the  nine  different  columns  of  figures, 
not  only  in  relation  to  its  own  element  over  the 
period  of  years  but  also  in  relation  to  each  of  the 
elements  of  the  other  eight  columns,  is  prac- 
tically an  impossibility  to  most  minds.  And 
yet  one  of  average  intelligence  can  easily  read 
the  trend  or  tendency  of  these  prices  of  different 
kinds  of  meats  when  interpreted  by  the  curves. 

WORD  DESIGNATIONS  OF  CURVES 

Not  only  from  the  point  of  view  of  interpretation 
but  also  of  mechanical  construction  the  chart  on 
page  96  is  recommended  for  close  study.  Note 
the  word  designations  of  the  curves  to  the  left 
and  right  of  the  vertical  scale  lines.  This  inser- 
tion of  the  word  designation  alongside  the  point 


Curve  and  Bar  Designations  99 

of  contact  of  the  curve  with  the  vertical  scale 
lines  lends  to  easy  reading  of  the  chart.  It 
requires,  however,  extending  the  space  between 
each  vertical  scale  line  and  its  respective  neat 
line,  and  this  is  not  always  possible.  In  such 
cases  the  curve  designations  with  their  word 
descriptions  should  be  placed  at  some  convenient 
place  on  tlie  framework  itself  as  a  sort  of  key  or 
legend.  Quite  frequently  a  good  place  for  the 
legend  will  be  found  to  be  just  beneath  the  bottom 
horizontal  line  and  above  or  between  the  foot- 
notes. 

The  different  designations  that  can  be  em- 
ployed for  curves  should  be  practiced  by  the 
student  until  he  has  acquired  facility  in  drawing 
them.  To  assist  liim  in  this  the  following  page 
of  designations  is  presented.  These  have  been 
made  considerably  larger  than  is  necessary  for 
the  curve  on  the  chart. 

THE    PEAK-TOP   CURVE 

The  student  is  cautioned  against  making  use  of 
what  is  called  the  "stairway"  curve.  This  juakes  a 
flat  or  step-like  contact  at  the  point  determined  by 
the  scale.  .\11  curves,  as  lias  been  said,  should 
approach  the  point  of  contact  slantingly  and 
direct  from  the  |)oirit  previously  touched  on  the 
vertical     line.     The    great    advantage    of    this 


Curve  and  Bar  Designations         101 

peak-top  curve  is  brought  out  on  charts  contain- 
ing two  or  more  curves  which  approach  each  other 
at  or  near  the  same  points.  In  such  cases  the  peak- 
top  permits  of  easy  separation  of  the  two  curves 
and  does  not  result  in  confusion  caused  by  in- 
ability to  follow  the  curves,  which  latter  is  inevit- 
able when  two  flat-top  or  stairway  curves  ap- 
proach each  other  at  the  scale  unit  points. 

DETERMINING   THE   SCALE   SPACING 

In  determining  the  vertical  space  a  number  of 
curves  should  occupy  every  one  of  the  columns  of 
figures  in  the  statistical  table  is  examined  to  ascer- 
tain the  lowest  and  highest  numbers  that  are  to 
be  charted.  That  is,  for  this  purpose  all  the  difi'er- 
ent  columns  representing  the  comparable  statis- 
tical elements  are  considered  as  if  they  were  only  a 
single  column. 

Take,  for  illustration,  the  table  of  the  chart  on 
page  96.  The  lowest  number  of  cents  represented 
in  any  one  of  all  .seven  columns  is  12.2  in  the  col- 
umn for  the  year  1918.  This  number  also  appears 
in  the  colunui  for  the  year  1915.  The  largest 
numl)er  of  cents  in  any  one  of  all  the  columns  is 
57.2  in  the  column  for  the  ^ear  1919.  Thus  the 
spread  for  all  the  numbers  in  all  the  columns  is 
from  12.2,  the  j)rice  of  plate  beef  in  1913  (also  in 
1915),  to  57.2,  the  price  of  bacon  in  1919,  or  a  max- 


102        Chartography  in  Ten  Lessons 

imum  spread  for  all  the  figures  of  45.  With  a  verti- 
cal scale  unit  of  5  this  spread  requires  at  least  ten 
squares  vertically  with  the  base  line  starting  at  the 
unit  10.  Starting  at  0  would  require  two  addi- 
tional squares  below  the  scale  unit  10,  but  if  this 
were  done  there  would  not  be  space  enough  any- 
where on  the  framework  for  the  inclusion  of  the 
statistical  table.  Our  squares  are  thus  more 
valuable  at  the  top,  so  we  provide  two  additional 
there  to  accommodate  the  table. 

UTILITY   OF  THE   CURVE   CHART 

By  this  time  the  student  should  have  become 
impressed  with  the  great  utility  of  the  curve 
method  in  chartography.  In  comparing  the 
tendency  over  a  period  of  time  of  two  or  more  dis- 
tinct but  related  statistical  elements  it  is  far 
superior  to  the  bar  method  in  chart  making  and 
incidentally  is  also  superior  to  the  statistical  me- 
thod. While  a  trained  statistician  could  interpret 
satisfactorily  the  tendency  from  a  study  of  col- 
umns of  figures,  no  one  else  could  perceive  the 
movement  as  clearly  as  it  is  convincingly  demon- 
strated by  curves  drawn  in  relation  to  each  other. 

This  is  particularly  true  when  more  than  two 
curves  representing  different  columns  of  figures  are 
compared,  as  in  the  chart  on  page  96.  These 
curves  not  only  show  the  variations  in  each  of  the 


Curve  and  Bar  Designations         103 

items  for  each  year  compared  with  the  other  years 
and  with  the  other  items  but  they  also  give  a 
comprehensive  perspective  of  the  entire  movement 
during  all  the  years;  they  show  the  status  of 
each  of  the  items  in  relation  to  every  other  item 
for  each  year  and  at  the  beginning  and  through 
to  the  end  of  the  period  of  time.  Thus  it  is  that 
chartography  can  be  said  to  "speak"  a  language 
easily  made  intelligible  to  the  mind  through  the 
eye. 

chartography  based  on  comparisons 

The  curve  also  strikingly  emphasizes  the  fact 
that  the  art  of  chartography  is  based  upon  rela- 
tions or  comparisons.  There  can  be  no  chart 
without  a  comparison  of  some  kind.  And  as  the 
very  nature  of  statistics  involves  a  relation  be- 
tween or  a  comparison  of  groups  of  facts,  it  is 
not  too  nmch  to  say  that  chartography  is  the  art 
best  adapted  to  expressing  this  clearly  and  con- 
cisely. 

"Comparison  is,  in  general,  the  final  goal  to- 
ward which  all  statistical  studies  tend,"  says  King, 
in  his  Elements  of  Statistical  Method.  "Com- 
parison is  necessary  to  give  us  clear  ideas  of  the 
relationship  of  things  in  time  and  space.  It  is  also 
essential  in  determining  whether  phenomena  are 
connected  or  independent  and  in  establishing 
relations  of  cause  and  effect.     We  may  wish  to 


104        Chartograpiiy  in  Ten  Lessons 

study:  1.  Changes  of  a  single  variable.  2.  The 
structure  of  different  groups.  3.  Changes  in  two  or 
more  variables." 

Brinton,  in  his  Graphic  Methods  for  Presenting 
Facts,  puts  it  this  way:  "One  of  a  business  man's 
chief  assets  is  his  ability  to  show  things  to  others 
in  their  true  proportions.  He  is  continually  mak- 
ing contrasts,  and  holding  up  for  comparison 
different  propositions  which  come  up  in  his  daily 
affairs.  The  graphic  method  lends  itself  admir- 
ably to  use  in  making  comparisons.  It  is  surpris- 
ing how  much  clearer  even  simple  comparisons  of 
only  two  or  three  items  will  appear  when  their 
numerical  value  is  put  in  graphic  form  rather 
than  in  figures." 

In  every  chart,  then,  a  comparison  or  relation  of 
some  kind  is  involved.  This  comparison  may  be 
with  the  same  statistical  element  for  two  or  more 
periods  of  time;  it  may  be  of  two  or  more  differ- 
ent elements  for  the  same  or  different  periods  of 
time.  It  may  be  a  comparison  of  total  or  abso- 
lute amounts,  of  increases  or  decreases,  of  the  rate 
of  change.  It  may  be  a  relation  of  one  or  m.ore 
elements  expressed  in  proportions  to  a  common 
total,  and  so  on. 

Graphic  methods  must,  of  course,  show  compar- 
able facts  only  and  these  in  their  true  relations 
and  prop>ortions  in  order  to  present  the  correct  sit- 


Curve  and  Bar  Designations         105 

nation.  They  represent  the  best  kno'^'n  scheme 
for  presenting  contrasts  and  in  this  way  indelibly 
impressing  their  significance  upon  the  mind.  Hav- 
ing recourse  to  curves  differently  constructed 
permits  some  of  these  comparisons  to  be  made 
much  more  clearly  than  if  the  chartographer 
were  limited  to  the  unbroken  or  straight  line 
curve. 

BAR    DESIGNATIONS 

DiflFerent  designations  for  different  statistical 
elements  or  factors  apply  with  equal  significance 
to  the  bar  as  to  the  curve  chart.  The  simplest 
designations  are  plain  black  and  white  which  are 
usually  employed  where  only  two  groups  of 
figures  or  statistical  elements  are  involved.  The 
plain  white  bar  is  secured  simply  by  outlining  it 
on  the  section  sheet  and  without  filling  it  in  with 
the  ink.  But  it  is  not  as  satisfactory  as  a  cross- 
hatched  bar,  that  is,  one  with  the  outline  filled 
in  by  drawing  liglit  diagonal  lines. 

One  use  of  designations  in  bar  charts  is  illus- 
trated in  the  cliart  on  page  106.  The  student 
should  write  out  on  i>ai)er  a  careful  analysis  of 
this  chart,  not  only  from  the  point  of  view  of  its 
construction  but  also  from  that  of  iiiteri)retation. 

Another  and  probably  the  most  common  use 
of  designations  in  bar  charts  is  illustrated  on 
page  107.   It  shows  the  employment  of  the  black 


OPERATING  REVENUES  AND  EXPENSE* 

PENNSYLVANIA  RAILROAD 


KlUloo*  of  B«Uara 


100  129 


«lw»n«<  trm  Bcpert*  of  R&ilrood 
te  latarvtsW  Oo^Nrca  Caaaiuian 


108        Chartography  in  Ten  Lessons 

and  white  as  parts  of  a  whole  bar.  In  this  chart 
the  total  freight  traffic  of  the  Norfolk  and  Western 
Railroad  Company  has  been  separated  on  tlie 
percentage  basis  between  bituminous  coal  and 
all  other  commodities  transported.  The  com- 
parison involved  is  expressed  as  a  ratio.  The 
changes  over  the  period  of  years  of  the  coal 
traffic  in  relation  to  the  total  traffic,  as  well  as 
also  in  relation  to  the  traffic  in  all  other  com- 
modities, is  seen  by  comparing  the  black  portions 
of  the  bars  with  the  total  bars,  reading  from  left 
to  right.  Similar  changes  in  the  proportion  of 
the  traffic  of  other  commodities  to  the  total 
freight  traffic  is  shown  by  comparing  the  white 
portions  of  the  bars  with  the  total  bars,  reading 
from  right  to  left  in  order  better  to  secure  an 
idea  of  the  differences  in  the  length  of  the  white 
sections.  The  proportion  of  each  designation 
to  the  total  bar  in  any  one  year  and  the  changes 
as  between  years  are  clearly  indicated. 

In  this  chart  each  of  the  series  of  horizontal 
bars  represents  by  100  per  cent  the  total  amount 
of  all  freight  traffic  for  each  of  the  designated 
years.  Consequently  all  the  bars  are  of  the  same 
length.  No  information  is  given  as  to  the 
numbers  representing  the  absolute  amount  of 
traffic  of  the  road,  which  it  may  naturally  be 
assumed  varied  in  the  different  years — it  may 


Curve  axd  Bar  Designations         109 

have  increased  or  decreased  from  year  to  year 
and  if  these  numbers  were  charted  they  would 
likely  give  bars  of  varying  lengths.  All  that  the 
chartographer  is  interested  in,  so  far  as  the  sta- 
tistics enlighten  him,  are  the  changes  in  the  pro- 
portion of  the  two  components  which  together 
comprise  the  total  freight  traffic  for  each  year. 

SOME  CHARACTERISTICS  OF  A  GOOD  BAR  CHART 

The  chart  on  page  107  is  a  good  illustration  of 
this  kind  of  a  bar  chart.  The  title  is  concise  and 
yet  comprehensive.  The  sub-title — that  of  the 
particular  railroad — is  well  placed  and  well 
spaced.  The  figures  for  the  years  are  directly 
under  each  other  and  are  spaced  sufficiently  from 
the  bars,  while  the  figures  for  the  black  and  white 
portions  of  the  bars  are  directly  in  proper  column 
form  on  each  of  the  six  bars.  The  reader  is  told 
at  the  top  of  the  framework  that  the  figures 
represent  j^er  cents,  and  at  the  bottom  among  the 
foot-notes  that  the  statistics  have  been  "Com- 
piled from  Rei)orts  of  the  Railroad  to  Interstate 
Commerce  Comjuission."  Tlie  group  of  bars  is 
.so  spaced  as  to  avoid  the  appearance  of  crowding. 
The  designations  of  the  bars  are  dearly  distin- 
guished between  "liitujiiinoiis  Coal"  and  "Other 
Commodities"  l)y  means  of  I  lie  legend  beneath 
the  bars.  The  neat  lines  j)roperly  frame  the 
.series  of  l)ars. 


Curve  and  Bar  Designations         111 

When  more  than  two  statistical  elements  have 
to  be  indicated  on  a  bar  the  chartographer  has 
recourse  to  an  almost  unlimited  number  of  differ- 
ent designations.  Some  of  these,  showTi  in  the 
chart  on  the  opposite  page,  indicate  the  extent 
to  which  variation  in  bar  designations  can  be 
carried.  The  effect  of  the  use  of  these  different 
designations  is  for  the  purpose,  of  course,  of 
causing  the  areas  to  stand  out  in  contrast  with 
each  other.  The  student  should  practice  until 
he  becomes  proficient  in  making  these  designa- 
tions. 

In  the  chart  on  page  89  (Lesson  VII)  and  in  the 
one  on  page  106  will  be  found  a  simj)le  device  and 
yet  a  valuable  aid  to  cliartography.  This  is  the 
word  designation  of  the  vertical  scale  unit  of  a 
curve  and  the  horizontal  scale  unit  of  a  bar  chart. 

In  the  chart  on  page  89  (Lesson  VII)  this 
designation  is  "Thousands  of  Immigrants."  By 
its  use  the  chartographer  is  able  to  drop  from  each 
of  the  vertical  scale  units  all  the  cii)hers  repre- 
senting thousands.  That  is,  instead  of  the  vertical 
scale  starting  with  the  unit  0,000  it  begins  with  6, 
the  interpreter  of  the  chart  knowing  frtun  having 
read  the  word  designation  that  this  unit  6  means 
6,000.  So  with  the  horizontal  scale  unit  of  the 
chart  on  page  106.  'I'hrrc  the  word  designation  is 
"Millions  of  Dollars"  and  this  permits  the  drop- 


112        Chartography  in  Ten  Lessons 

ping  of  six  ciphers  from  each  of  the  liorizontal 
scale  units — it  allows  the  scale  to  begin  with 
the  unit  100  instead  of  requiring  100,000,000. 
To  reproduce  the  additional  six  ciphers  after  each 
one  of  the  horizontal  scale  units  would  over- 
burden the  horizontal  scale  line  with  figures  even 
if  sjiace  could  be  found  for  all  of  them. 

IMaking  use  of  the  word  designation  of  the 
scale  so  as  to  drop  the  ciphers  from  the  scale  line 
itself  has  many  advantages  and  should  always  be 
employed  where  the  numbers  represented  are 
more  than  three  digits,  that  is,  thousands  and 
over.  The  designation  should  be  clearly  pre- 
sented in  an  easily  observable  place  on  the  chart, 
even  when  the  table  of  figures  would  seem  to 
make  this  unnecessary,  so  that  the  chart  can  be 
quickly  read  and  easily  understood  without 
reference  to  the  statistics  from  which  it  is  made. 
Usually  the  best  position  for  the  word  designation 
is  just  beneath  the  top  neat  line  and  centered 
above  the  horizontal  scale  line. 

QUESTIONS  FOR  SELF-EXAMINATION 

1.  What  are  the  advantages  of  various  designations  for 
different  curves? 

2.  Describe  the  peak-top  curve. 

3.  How  is  the  scale  spacing  determined.'' 

4.  Describe  the  utility  of  a  curve  chart. 

5.  What  is  the  basis  of  chartography.'' 

6.  Discuss  the  uses  of  various  designations  for  different 
bars. 


LESSON  IX 

Value  of  Statistics  to  Chartography 

The  Statistical  Table — Aids  in  Reading  the 
Table — The  Substitution  of  Ciphers — The 
Table  of  Ratios— Building  Up  A  Table— The 
Percentage  Increase  and  Decrease — The  Zero 
Line — The  Arithmetic  Average — The  Misuse 
of  the  Average — Statistical  Class  Limits. 

It  should  be  clear  by  this  time  that  a  most 
important  asset  in  the  practice  of  chartography 
is  a  knowledfje  of  statistics.  The  mere  mechani- 
cal act  of  drawing  lines  and  curves  and  bars  on 
section  paper  is  the  work  of  the  draftsman  and 
does  not  of  itself  make  a  chartographer.  In 
these  lessons  it  has  been  assumed  that  the  infor- 
mation is  already  at  hand  in  proper  form  for  the 
drawing  of  the  chart — that  the  collection  and 
comj)ilati()n  of  the  statistics  have  been  correctly 
done  and  that  the  figures  have  been  checked 
and  verified  so  that  there  is  no  question  as  to  their 
accuracy  and  trustwortliiness. 

This  assum{)tion  has  been  necessary  for  the 
reason  that  statistics  are  a  distinct  field  of  study  in 
themselves,  with  sub-divisions  as  to  metlio<ls  of 
collection,  of  comjiilatiorj,  of  tabulation,  of  comjju- 
tation,  of  arrangement,  of  presentation,  of  inter- 
ns 


114        Chartography  in  Ten  Lessons 

pretation,  and  so  on.  This  field  is  entirely  too 
extensive  to  be  presented  in  these  Lessons  even 
in  merest  outline,  and  for  a  knowledge  of  its 
principles  the  student  should  have  recourse  to 
standard  books  on  the  subject.  All  that  can  be 
done  here  is  to  make  the  briefest  reference  to  a  few 
only  of  its  features  which  most  vitally  concern 
the  beginner  in  chartography. 

THE   STATISTICAL  TABLE 

Conspicuous  among  these  is  the  arrangement  of 
the  statistical  elements  in  the  table.  The  prin- 
ciples underlying  this  have  necessarily  been  dis- 
cussed briefly  in  preceding  Lessons.  But  there 
is  one  other  point  in  particular  to  which  attention 
must  be  called.  This  is  the  more  or  less  common 
practice — fortunately  it  is  becoming  less  common 
as  the  rules  of  good  chartography  become  more 
widely  disseminated  and  better  known — for 
charts  to  appear  in  otherwise  first-class  publica- 
tions with  the  statistical  table  having  the  latest 
date  at  the  top  and  with  the  earliest  period  of  time 
at  the  bottom  of  the  column. 

A  chart  made  from  a  table  arranged  in  this 
way  reads  backwards  from  the  latest  to  the 
earliest  year.  In  order  to  interpret  it  from  the 
earliest  year  and  in  sequence  of  time  it  has  to  be 
read  from  right  to  left,  which  is  the  wrong  way  to 


Value  of  Statistics  to  Chartography  115 

read  a  chart.  Invariably  this  arrangement  is  at 
first  glance  misread,  as  the  natural  inclination  of 
the  reader  is  to  assume  that  years  are  arranged 
in  proper  sequence.  WTiere  they  are  not  so  ar- 
ranged too  much  time  is  lost  before  this  is  realized. 
The  first  impression  on  the  interpreter  of  the 
chart  in  such  cases  is  exactly  the  reverse  of  that 
intended  and  which  would  have  been  received 
by  him  if  the  correct  method  of  arranging  the 
statistical  elements  in  table  form  had  been  fol- 
lowed. In  consequence,  one  of  the  fundamental 
purposes  of  the  chart  method  of  disseminating 
knowledge  is  violated.  Such  a  practice  should 
not  be  indulged  in  even  in  exceptional  cases. 

reconstructing  the  table 

Whenever  the  chartographer  has  a  table  of 
figures  to  chart  in  which  the  latest  year  or  period 
of  time  appears  at  the  top  of  the  column,  he  should 
rearrange  or  reconstruct  the  tabic  in  correct  col- 
umn form  with  the  earliest  year  at  the  top  before 
he  begins  planning  his  chart. 

The  justification  for  presenting  the  latest  year 
first  in  tlie  column  is  that  it  is  of  greater  impor- 
tance compared  with  the  other  years  recorded. 
As  a  mattf'r  of  fart,  no  one  year  in  a  series  of  years 
that  charts  a  tendency  is  of  any  greater  impor- 
tance than  the  other  years.     It  may  be  of  greater 


116        Chartography  in  Ten  Lessons 

importance  in  the  mind  of  some  particular  indi- 
vidual or  individuals  as  to  the  significance  of  the 
data  it  discloses  but  in  itself  as  a  year  it  is  only  of 
equal  importance  with  every  other  year.  Besides, 
chartography  offers  other  and  much  better 
methods  for  placing  emphasis  on  particular  statis- 
tical elements. 

AIDS   IN   READING   THE   TABLE 

It  may  be  advisable,  where  large  numbers  are 
the  basis  of  a  chart,  to  substitute  ciphers  as  the 
last  two  figures  in  tens  of  thousands,  the  last 
three  in  hundreds  of  thousands,  and  the  last  five 
in  millions.  By  raising  or  lowering  the  last 
preceding  digit  before  the  cipher,  sufiicient 
accuracy  is  obtained  for  the  purpose  of  most 
cha  ts.  The  advantage  of  this  is  that  the  ciphers 
enable  the  mind  to  grasp  more  quickly  the  signifi- 
cance of  the  numbers.  In  financial  statements, 
however,  this  practice  has  objections. 

Necessary  space  on  the  chart  for  the  columns  of 
figures  can  sometimes  be  secured  by  dropping 
entirely  the  last  three  or  six  digits  and  substituting 
at  the  head  of  the  columns  a  word  description  of 
the  amount  represented,  such  as  thousands  or 
m  illions  and  so  on  as  the  case  may  be.  This  elimi- 
nates the  confusion  to  the  eye  of  numerous  digits. 
While  this  practice  is  not  only  admissible  but 
also  advisable  in  designations  of  the  scales  it  should 


Valxje  of  Statistics  to  Chartography  117 

not  be  allowed  to  become  general  in  tabulations, 
not  even  where  the  value  or  volume  or  quantity  is 
so  large  as  to  run  into  seven  or  more  digits,  as  long 
as  there  is  space  on  the  chart  to  show  the  complete 
numbers  without  crowding. 

Assistance  in  the  direction  of  facilitating  the 
rapid  reading  of  a  statistical  table  and  in  enabling 
a  quicker  grasp  of  its  significance,  is  rendered  in 
cases  of  long  columns  of  figures  by  breaking  up 
the  numbers  into  groups  of  fives  with  double  the 
space  separating  each  group.  For  illustration, 
instead  of  presenting  the  table  on  the  chart  like 
this: 

Year  Population 

1900  75,994,575 

1901  77,747,402 

1902  79,305,396 

1903  80,983,390 

1904  82,001,384 

1905  84,219,378 
1900  85,837,372 

1 907  87,455,300 

1908  89,07.3,300 

1909  90,091, .354 

1910  92,.309.348 

1911  93,927,342 

1912  95,545.330 

1913  97,I03,.3.30 

1914  98,78 1, .324 

1915  100,399,318 
1910  102,017,312 


Il8       Chartography  in  Ten  Lessons 
It  might  better  be  presented  ag  follows; 

Year  Population 

1900  76,000,000 

1901  77,700,000 

1902  79,400,000 

1903  81,000,000 

1904  82,600,000 

1905  84,200,000 

1906  85,800,000 

1907  87,500,000 

1908  89,100,000 

1909  90,700,000 

1910  92,300,000 

1911  93,900,000 

1912  95,500,000 

1913  97,200,000 

1914  98,800,000 

1915  100,400,000 

1916  102,000,000 

These  figures  represent  the  population  of 
continental  United  States  as  reported  by  the 
Bureau  of  the  Census  of  the  United  States  Govern- 
ment in  its  bulletin  on  mortality  statistics  for 
1916.  Using  them  as  a  basis,  the  student  is 
instructed  to  draw  with  a  lead  pencil  a  curve  or 
bar  chart,  whichever  he  determines,  applying  to 
his  task  the  instructions  he  has  received  up  to  this 
point. 


Value  of  Statistics  to  Chartography  lid 

THE  substitution  OF  CIPHERS 

This  substitution  of  ciphers  for  other  digits  in 
large  numbers  does  not  affect  the  accuracy  of  the 
chart  for  the  reason  that  the  change  made  by  it 
in  any  number  is  so  slight,  compared  with  its 
total,  as  to  be  lost  in  the  results  of  the  applica- 
tion of  the  scale  unit  to  its  measurement.  Be- 
sides, it  has  a  distinct  advantage  in  that  it  does 
not  accord  to  the  statistics  any  greater  import- 
ance than  the  method  of  their  compilation  war- 
rants. No  one  who  is  familiar  with  the  methods 
of  taking  or  enumerating  the  decennial  census  of 
the  population  of  the  United  States  and  of  esti- 
mating its  growth  for  intermediate  years  believes 
for  a  single  moment  that  this  population,  say,  in 
1916,  was  exactly  102,017,312  to  the  last  digit  of 
accuracy.  While  no  criticsm  of  these  methods  is 
here  intended,  it  is  bul  stating  the  fact  that  they 
are  not  so  perfect  as  to  record  to  the  last  figure 
the  exact  population.  Most  statistical  tables  at 
best  are  api)roximations  and  do  not  represent 
absolutely  accurate  and  indisi)utablc  facts  to  the 
point  of  minute  measurement. 

All  that  can  be  expected  of  chartography  is  that 
it  indicate  clearly  the  general  trend  or  tendency  of 
statistical  elements.  The  cliartogra|)her  should 
be  on  his  guard  against  i>ermitting  the  curve  or 
bar  to  convey  an  impression  of  a  greater  degree  of 


120       Chartography  in  Ten  Lessons 

accuracy   than   is  warranted  by  the  statistical 
information. 

THE   TABLE   OF   RATIOS 

In  deahng  with  tables  of  ratios  it  is  always 
advantageous  to  carry  the  digits  at  least  one  place 
beyond  the  decimal  point.  The  advisability  of 
this  should  be  so  clear  as  not  to  need  to  be  dis- 
cussed. If,  for  instance,  by  not  including  the 
last  digit  of  the  two  ratios  67.6  and  32.4  of  the 
1912  bar  in  the  chart  on  page  107  (Lesson  VIII) 
each  portion  of  the  whole  bar  falls  short  of  its 
correct  measurement  and  the  total  100  per  cent 
bar  is  incomplete.  It  is  hardly  ever  necessary 
to  carry  the  digits  further  than  two  decimals  and 
in  most  cases  one  digit  beyond  the  decimal  point 
answers  all  practical  purposes. 

Frequently  decimals  exceeding  one-half  may 
be  raised  to  a  whole  number  and  under  one-half 
lowered  to  a  cipher.  Where  the  digit  is  exactly 
one-half  whether  it  is  raised  or  lowered  will 
depend  upon  the  particular  circumstances.  Per- 
centages or  ratios  are  a  problem  in  mathematics 
and  it  is  to  that  science  the  student  should  have 
recourse  for  more  complete  knowledge  of  the 
principles  involved. 

As  percentages  or  ratios  are  derivative  figures 
it  is  of  advantage,  if  it  does  not  over  burden 
the  chart,  to  place  also  on  the  framework  the 


Value  of  Statistics  to  Chartography  121 

original  figures  from  which  they  are  derived. 
Where  a  choice  as  to  exclusion  has  to  be  made  it 
should  be  in  favor  of  the  retention  on  the  chart 
of  the  derivative  figures  upon  which  it  is  based. 

BUILDING   UP  a   table 

Both  the  original  and  their  derivative  figures 
appear  in  the  table  of  the  chart  on  page  122, 
This  chart  also  illustrates  the  use  of  the  ciu-ve  in 
expressing  ratio.  The  problem  is  to  show  the 
income  of  the  Pennsylvania  Railroad  Company 
in  relation  to  its  securities,  that  is,  the  rate  earned 
by  the  latter  for  each  year  from  1909  to  1916, 
both  inclusive.  The  basal  information  as  to 
securities  and  income  was  secured  from  the  annual 
reports  of  the  company  filed  with  the  Interstate 
Commerce  Commission  in  AVashington,  D.  C. 

The  amount  of  bonds  representing  funded  debt 
and  the  capital  stock  were  added  to  ascertain 
the  total  of  all  securities  for  each  of  the  years. 
This  gives  the  second  column  of  figures  in  the 
table  to  the  chart.  In  order  to  ascertain  the 
total  income  that  is  properly  related  to  these 
securities  the  amount  of  interest  paid  on  funded 
debt  was  added  to  net  corporate  income  for  each 
year,  which  gives  the  third  column.  This  in- 
formation enables  us  to  ascertain  the  rate  of 
income  each  year  Ijy  dividing  the  amounts  repre- 


RATE  OF  INCOME  ON  RAILWAY  SECURITIES 


PENNSYLVANIA   R.   R. 
in*  i«i»  Mil  im  IMS  lilt  uu  t<ic 


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492,443 

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401,677 

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Value  of  Statistics  to  Chartography  123 

senting  capital  obligations  into  the  amounts 
representing  net  corporate  income  and  interest 
for  each  of  the  corresponding  years.  The  result 
is  the  fourth  or  ratio  column  of  the  table.  The 
other  column  of  ratios — the  seventh  of  the  table 
— is  ascertained  by  dividing  the  amounts  repre- 
senting capital  stock  into  the  amounts  represent- 
ing net  corporate  income. 

It  should  be  noted  that  the  only  comparison 
made  by  the  two  curves  of  the  chart  is  based 
upon  the  two  columns  of  ratio  figures.  It  would 
better  assist  comparison  in  the  statistical  table 
if  these  two  columns  were  placed  alongside  each 
other,  but  this  cannot  be  accomplished  with 
clearness  in  reading  without  making  another 
table  with  the  column  of  years  duplicated  and 
with  awkward  headings  above  each  ratio  column. 
This  latter  is  due  to  the  words  expressing  the 
exact  meaning  of  the  ratio  column  taking  up  a 
great  deal  more  space  in  width  tlian  is  occupied 
by  the  three  digits  and  the  decimal  {)(»int.  Thus 
to  place  adjacent  to  each  other  the  columns  that 
are  compared  is  likely  to  comniit  an  ofFense  more 
.serious  than  is  the  value  of  the  advantage  to  be 
gained. 

THE  percentage  INCREA.SE  OR  DECREASE 

Quite  a  different  percentage  chart  is  presented 
on  page  124.     It  shows  the  rate  or  per  cent  of  in- 


PRIMCIPAL  ITEMS  OF  OPERATING  EXPENSES.   1008-1013 


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Value  of  Statistics  to  Chartography  125 

crease  or  decrease.  This  arithmetical  principle  is  a 
most  valuable  aid  to  the  chartographer,  for  without 
it  many  curve  charts  that  are  now  possible  could 
not  be  made.  This  is  true  in  most  cases  where 
the  difference  between  the  numbers  to  be  com- 
pared is  considerable,  that  is,  where  some  are 
large  and  the  others  small  numbers,  as  a  chart 
of  these  absolute  amounts  is  impossible  owing  to 
the  requirements  of  space  necessarj^  to  indicate 
the  "spread"  between  the  highest  and  the  lowest. 
But  by  resolving  these  varying  amounts  into  per 
cent  increases  or  decreases,  as  the  figures  deter- 
mine arithmetically,  statistical  elements  are 
secured  which  permit  of  a  common  measurement 
and  in  consequence  of  a  comparison  of  relative 
movements  over  a  period  of  years. 

The  percentage  increase  or  decrease  in  our  chart 
of  each  element  for  each  year  from  1908  to  1913  is 
based  upon  the  amount  for  1908.  In  consequence 
everj'  curve  starts  frojn  the  same  point  at  zero  on 
the  1908  vertical  line,  because  it  is  plain  that 
there  could  l)e  no  increase  in  1908  over  1908.  As 
the  per  cent  figures  for  every  element  show  a 
decrease  in  1909  over  190H  every  curve  extends 
downward  below  the  zero  line  to  the  respective 
points  of  contact  with  tlic  vertical  line  for  1909, 
For  each  of  the  following  years  the  curves 
separate   more  f)r  less  widely  according    to  the 


126        Chartography  in  Ten  Lessons 

tendency    as    indicated   by   the  figures  for   the 
different  elements. 

Taking  the  year  1913  for  illustration,  there  is 
an  increase  over  1908  in  every  one  of  the  prin- 
cipal operating  expense  items.  It  also  shows 
that  the  expense  of  buildings,  fixtures,  and  so  on 
had  increased  faster  relatively  than  that  of  steam 
locomotives,  or  of  rails  and  ties,  or  of  wages,  and 
so  on;  that  the  expense  of  passenger  cars  had 
increased  less  rapidly  than  that  of  any  of  the 
other  items,  and  that  this  expense  was  greater  in 
1913  than  in  1908. 

THE   ZERO   LINE 

The  chart  on  page  124  presents  also  the  zero  line 
feature  of  chartography  based  upon  percentage 
increase  or  decrease  figures  and  not  on  absolute 
amounts.  It  is  one  that  the  student  is  likely  to 
have  frequent  occasions  to  make  use  of.  This  line 
is  indicated  by  the  cipher  designation  on  the 
vertical  scale  lines. 

The  zero  line  is  in  reality  the  base  from  which 
the  curves  move  up  or  down  as  the  numbers  of 
the  statistical  table  and  the  scale  units  determine. 
It  practically  represents  the  amounts  of  each  of 
the  eight  elements  in  the  year  1908  as  indicated  by 
the  line  drawn  horizontally  across  the  chart,  for 
the  increase  or  decrease  is  "over"  that  year  or 
line.     In    other    words,    the    movement    of    the 


Value  of  Statistics  to  Chartography  127 

curves  for  any  one  and  all  of  the  six  years  in  rela- 
tion to  the  zero  line  is  determined  by  the  rela- 
tion of  the  amount  in  each  year  to  the  amount  in 
1908.  Thus  the  fluctuations  in  the  curves  from 
year  to  year  should  be  read  or  measured  from  this 
zero  line  and  not  from  the  slopes  of  the  curves 
themselves. 

Facility  in  the  interpretation  of  such  a  chart  is 
aided  if  it  is  clearly  indicated  that  all  the  move- 
ments of  the  curves  above  the  zero  line  mean 
increases  over  the  base  year  and  below  that  line 
decreases  compared  with  that  year.  This  is  accom- 
plished by  inserting  the  words  "Increase"  and 
"Decrease"  alongside  the  vertical  scale  lines  on 
either  side  of  the  zero  line.  This  shows  clearly  that 
the  vertical  scale  reads  upward  from  the  zero  line 
for  increases  and  downward  for  decreases. 

Assistance  in  the  clear  interpretation  of  such  a 
chart  is  also  rendered  by  making  the  zero  line 
slightly  heavier  or  wider  than  the  other  horizontal 
lines  connecting  at  other  units  of  the  vertical 
scale  lines  and  at  tlie  same  time  not  as  heavy  or  as 
wide  as  the  curve  or  curves  themselves.  This 
wider  zero  line  calls  tlie  reader's  attention  to  the 
fact  that  he  nnist  interpret  the  movements  of  the 
curves  from  the  zero  and  not  from  tlu*  lowest  or 
base  line. 

In  cases  where  the  figures  to  be  charted  show 


128        Chartography  in  Ten  Lessons 

no  decreases  and  in  consequence  it  is  not  necessary 
to  extend  the  curves  below  the  zero  line,  then 
this  line  becomes  also  the  lowest  or  base  line  at  the 
bottom  of  the  chart  and  all  the  movements  of 
the  curves  are  above  that  line.  In  such  cases  it  is 
not  necessary  to  employ  the  terms  "Increase"  and 
"Decrease"  above  and  below  the  zero  line.  Nor 
is  it  necessary  in  such  cases  that  the  zero  line  be 
made  wider  than  the  other  horizontal  lines. 

While  the  chart  on  page  124  designates  with  a 
cipher  the  horizontal  line  from  which  the  move- 
ments of  the  curves  are  measured,  as  a  matter  of 
fact  this  line  is  not  a  zero  line  but  a  100  per  cent 
line.  This  is  true  arithmetically  for  the  reason 
that  in  reality  it  represents  the  total  amount  of 
each  element  or  item  for  1908.  These  were  taken 
as  the  base  from  which  the  figures  for  each  of 
the  other  years  were  ascertained.  Arithmetic 
exactness  requires  that  this  line  be  designated  as 
a  100  and  not  a  0  line.  But  in  this  case  chartog- 
raphy takes  liberties  with  arithmetic  for  the  sake 
of  securing  greater  clearness  in  interpretation. 
Experience  has  taught  that  because  of  the  general 
lack  of  knowledge  on  the  part  of  many  of  those 
for  whom  charts  are  prepared,  confusion  leading  to 
misinterpretation,  and  this  to  misinformation, 
results  whenever  the  100  per  cent  designation 
is  employed  in  place  of  the  cipher. 


Value  of  Statistics  to  Chartography  129 

THE   arithmetic  AVERAGE 

In  the  chart  on  page  124  the  basis  upon  which 
the  respective  percentages  have  been  computed 
is,  as  has  been  said,  an  amount  for  a  single  year. 
Wherever  possible  this  basis  should  be  the  average 
of  the  amounts  for  a  number  of  years,  and  this  is 
nearly  always  feasible  when  the  number  of  years  in 
the  table  comprises  ten  or  more.  This  average  is 
ascertained  by  adding  the  amounts  for  the  years 
selected  and  dividing  the  total  thus  obtained  by 
the  number  of  these  years.  The  percentage  in- 
crease or  decrea.se  is  then  computed  for  each  of 
the  years  from  this  average  amount.  This  is  not 
advisable  for  the  statistics  in  the  chart  on  page 
124,  as  the  number  of  years  is  only  six.  In  those 
cases  where  it  can  l)e  done  there  will  likely  be 
found  a  material  difference  between  the  move- 
ments of  curves  over  a  period  of  years  thus  dis- 
clo.sed  compared  with  the  movements  shown  with 
only  a  single  year  as  the  ba.se. 

The  advantage  of  taking  the  average  for  a 
number  of  years  as  the  base  for  comj)uting  in- 
creases or  dccrea.ses  is  found  in  the  fact  that  this 
average  smooths  out  the  irregularities  of  high  and 
low  or  of  large  and  small  amounts  which  nuiy  have 
been  compri.sed  in  the  different  years.  If  a 
single  year  only  is  u.sed  as  the  base  it  may  be  that 
in    that    particular   year    unusual    influences    or 


130        Chartography  in  Ten  Lessons 

forces  werc  at  work  to  change  unduly  its  total  in 
comparison  with  preceding  or  following  years 
and  in  consequence  it  is  out  of  normal  relation  to 
the  amounts  of  the  other  years. 

An  illustration  of  this  as  to  many  phases  of 
railway  operation,  for  instance,  is  the  fiscal  year 
1908  extending  from  July  1,  1907,  to  June  30, 
1908,  both  inclusive.  The  records  for  that  fiscal 
year  include  the  effects  of  the  panic  in  the  latter 
part  of  the  calendar  year  1907.  The  railroads 
were  very  seriously  affected  by  this  disturbance 
in  business  and  financial  conditions  and  their 
traffic  and  revenue  fell  off  strikingly.  In  con- 
sequence, any  comparison  of  the  operations  and 
finances  of  subsequent  years  based  upon  the  single 
year  1908  would  show  tendencies  that  might  not 
and  would  not  be  shown  if  a  year  that  did  not 
record  a  panic  was  used  as  the  base.  Averaging 
a  number  of  years  escapes  this  possibility  of 
statistical  error  and  in  consequence  avoids 
misrepresentation  in  chartography. 

The  proper  Use  of  the  average  is  an  important 
asset  to  the  chartographer.  This  average  reper- 
sents  or  indicates  the  usual  or  common  occurrence 
or  status.  It  is,  primarily,  as  has  been  stated,  a 
problem  of  arithmetic.  Quite  often,  if  not  always, 
it  is  simply  an  arithmetical  standard,  non-existent 
in  actual  reality  and  yet  one  around  which  other 


Value  of  Statistics  to  Chartography  131 

facts  tend  to  approximate  or  conform  and  by 
which  they  are  measured  or  compared.  Such, 
for  instance,  as  the  average  height  of  men,  or 
the  average  price  of  a  pound  of  bacon,  and  so  on. 

the  misuse  of  the  average 

The  average  can  be  as  much  of  a  sinner  when 
improperly  made  use  of  as  it  is  a  saint  when 
properly  employed.  To  the  chartographer  the 
use  of  the  average  has  its  pitfalls  against  which  he 
must  be  constantly  on  his  guard.  While  it  is 
indispensable  at  times,  it  has  its  limitations  and 
shortcomings  and  these  must  be  known  if  he  is 
to  make  the  best  use  of  it  and  not  be  inveigled 
by  its  attractions  into  grievous  errors. 

Quite  frequently  the  average  comprises  ele- 
ments radically  different  from  each  other  whose 
irregularities  or  dissiniilarities  have  disapi)eared 
or  been  smoothed  out  to  such  an  extent  that  it 
does  not  represent  any  measurable  status  or  even 
ai)proximate  situation  of  the  actual  facts,  and  in 
consequence  can  have  no  other  effect  than  to  mis- 
lead. This  is  illustrated,  for  instance,  in  statistics 
giving  the  average  amount  of  stock  held  i)er 
stockholder  in  the  railways  of  the  I'nited  States. 

In  1914  this  average  was  staled  iis  $1.S,958. 
It  was  obtaiiie<l  by  dividing  the  total  iium})er  of 
stockholders — 022,284 — into  the  total  |)ar  value 


132        Chartography  in  Ten  Lessons 

capital  stock  outstanding— $8,685,764,000.  Of 
course,  such  an  average  is  absolutely  meaningless. 
It  is  merely  an  arithmetic  average.  No  such 
amount  of  stock  approaches  even  in  the  slightest 
degree  to  the  actual  facts  in  the  case.  The 
fallacy  in  any  practical  use  of  this  average  can  be 
demonstrated  by  a  simple  illustration  from  almost 
any  railroad. 

Let  us  take  the  Wabash  for  an  example.  In 
1915  a  single  stockholder — the  Equitable  Trust 
Company — owned  $28,744,000  of  the  stock  of 
this  railroad.  With  nine  others,  these  ten  largest 
stockholders  together  held  $59,449,200  of  the 
stock,  or  more  than  sixty-four  per  cent — nearly 
two-thirds.  In  view  of  these  very  large  single 
holdings  of  stock  by  a  very  small  number  of 
stockholders — these  ten  owning  by  themselves 
an  average  of  $5,944,920 — any  arithmetical  com- 
putation representing  the  average  amount  held 
by  each  stockholder  cannot  fairly  represent  the 
situation  as  to  the  ownership  of  stock  in  the 
Wabash  Railroad  Company. 

THE    STATISTICAL    CLASS    LIMITS 

In  such  cases  as  this  instead  of  making  use  of 
a  meaningless  average  there  is  the  possibility  of 
recourse  to  a  separation  of  a  group  of  figures  into 
class  limits  in  order  that  the  facts  of  a  given  situa- 


Value  of  Statistics  to  Chartography  133 

tion  may  be  more  accurately  presented.  This 
should  always  be  taken  advantage  of  whenever 
possible. 

Applied  to  the  preceding  illustration  it  simply 
means  the  separation  of  the  total  number  of 
stockholders  into  groups  or  classes  according  to 
selected  amounts  of  stock  held.  The  first  step 
in  this  statistical  process  is  to  determine  upon 
the  limitations  for  the  different  classes.  These 
are  purely  arbitrary'.  To  obtain  them,  round 
numbers  are  most  desira})le,  as  these  give  clear 
cut  groups.  These  numerals  form  what  are 
technically  known  as  boundary  lines  of  the  classes. 

The  difference  between  them  is  called  statis- 
tically the  class  interval.  These  class  intervals 
should  all  be  equal  or  uniform. 

The  number  of  cla.sses  and  the  inmiber  in 
eacli  class  become  statistically  what  is  called  a 
frequency  table. 

By  thus  di.ssecting  the  statistics  a  number  of 
very''  interesting  and  iiighly  important  facts  is 
usually  disclosed  which  the  presentation  of  the 
average  does  not  indicate  as  being  present.  A 
knowlwlgc  of  these  facts  is  essential  to  a  correct 
and  complete  i)rescntation  of  the  actual  situation. 

These  facts  indicate  that  the  chartographer 
must  exercise  his  best  judgment  in  the  i)resen- 
tation  of  the  average.     He  cannot  be  permitted 


134        Chartography  in  Ten  Lessons 

to  excuse  himself  by  hiding  behind  statistics. 
Charts  that  reflect  inaccuracies  and  irregulari- 
ties of  mathematical  computation  to  the  extent 
of  being  misleading  cannot  be  explained  away 
because,  in  truth,  they  never  should  have  been 
made.  This  is  a  high  standard  to  attain,  for 
quite  often  the  chartographer  must  depend  almost 
entirely  upon  his  statistics  for  a  truthful  presen- 
tation of  the  facts,  and  if  the  statistics  are  faulty 
it  seems  rather  unfair  to  hold  the  chartographer 
to  strict  responsibility  for  any  misleading  result. 
Nevertheless,  the  chartographer  should  be  as 
scrupulous  and  as  exacting  in  the  use  of  statistics 
as  in  the  use  of  the  English  language  in  maintain- 
ing a  high  standard  for  truthfulness  and  exactness. 

A  sufficient  variety  of  curve  and  bar  charts 
have  been  presented  in  the  preceding  Lessons  to 
impress  upon  the  student  of  chartography  that 
his  most  important  task  is  the  planning  of  the 
chart.  It  should  be  done  before  he  touches  pen 
to  paper  in  beginning  the  drawing  of  the  chart. 
With  this  planning  successfully  accomplished  the 
remaining  details  of  the  work  of  execution  or 
construction  becomes  a  relatively  simple  matter. 

In  this  planning  the  student  should  first  know 
thoroughly  the  real  meaning  or  significance  of 
the  table  of  statistics  he  is  to  chart — he  must 
"see"  clearly  the  vital  point  of  comparison  the 


Value  of  Statistics  to  Chartography  135 

chart  is  to  bring  out.  It  is  of  advantage  in  com- 
prehending this  point  if  the  student  will  roughly 
sketch  several  different  charts,  both  curve  and 
bar,  before  he  attempts  to  lay  out  the  curve  or 
bar  in  ink.  He  will  be  surprised  at  the  difference 
in  results  shown  by  the  various  methods,  and 
can  then  select  the  one  which  best  illustrates  the 
significance  of  the  statistics.  More  time  rela- 
tively should  be  given  to  the  planning  than  to 
the  actual  drawing  of  the  chart.  The  time 
devoted  to  the  latter  will  be  greatly  shortened 
if  the  planning  has  been  done  correctly.  Be- 
sides, it  will  also  save  time  lost  through  changes 
and  alterations  usually  made  necessary  where  the 
planning  has  been  neglected. 


QUESTIONS  FOR  SELF-EXAMINATION 

1.  What  is  the  value  of  statistics  to  chartography? 

2.  What  is  the  statistical  table?  How  should  it  be 
arranged? 

3.  Describe  some  of  the  technical  aids  to  the  interpreta- 
tion of  a  table  of  statistics. 

4.  What  are  ratios?  How  are  they  computed?  How 
arranged  in  table  form? 

5.  Describe  the  construction  of  a  statistical  table. 

6.  What  are  the  important  differences  between  ratios 
and  percentage  increases  or  decreases? 

7.  Of  what  value  to  the  chartographer  are  percentage 
increases  or  decreases? 

8.  Describe  the  zero  line  and  its  use  in  charts  showing 
percentage  increases  or  decreases. 

9.  What  is  the  average?  How  is  it  computed?  Describe 
its  advantages  and  disadvantages. 

10.  What  are  statistical  class  limits?  What  are  boun- 
dary lines  of  the  classes?  What  is  the  class  interval?  A 
frequency  table? 


1S6 


LESSON  X 

Primary  Principles  of  Chartography 

Planning  the  Chart — Importance  of  the  Right 
Method — Essentials  of  Good  Chart  Making — 
Planning  the  Size  of  the  Chart — Planning  a 
Reduction  in  Size — The  Reducing  Glass — 
The  French   Curves — Checking  up  the  Chart. 

Chart-making  for  commercial  and  other  pur- 
poses is  still  in  its  infancy  and  in  consequence 
has  not  yet  been  systematized.  Statisticians  who 
are  employing  it  to  an  increasing  extent  as  an 
aid  in  the  presentation  of  facts  are  in  disagree- 
ment, or  rather  are  not  in  accord,  as  to  the 
superiority  of  different  methods.  Give  a  group 
of  statisticians  who  are  also  familiar  with  chartog- 
raphy a  .set  of  figures  to  chart  and  there  will 
likely  be  as  many  different  kinds  of  charts  widely 
divergent  in  methods  as  there  are  statisticians. 
Thus  the  same  information  will  be  charted  in 
many  different  ways.  While  variety  in  charting 
is  possible  where  numerous  illustrations  must  be 
made,  at  the  sanir  time  sonic  mclhoris  are  better 
than  others  in  bringing  out  the  farts  more  clearly. 
Variety  of  effect  is  permi.ssible  and  sometimes 
desirable  in  order  to  avoid  monotony  in  presen- 
tation and  to  retain  attention. 

187 


138        Chartography  in  Ten  Lessons 

a  choice  of  methods 

The  value  of  the  chart  method  being  in  ex- 
pressing clearly  the  meaning  of  a  statistical  table, 
the  problem  of  the  chartographer  is  to  select  the 
one  method  from  among  the  many  that  will  best 
express  this  meaning.  Particularly  is  this  true  in 
the  use  of  charts  by  the  large  corporation.  Pre- 
pared usually  for  the  executive  whose  time  is 
limited  and  of  great  value,  the  chart  must  be  so 
drawn  as  to  give  to  him  instantly  the  true  sig- 
nijBcance  of  a  mass  of  statistics  which  he  has  not 
the  time  to  analyze  in  their  details.  The  eflBcient 
and  successful  executive  must  decide  quickly  and 
of  course  correctly.  The  information  furnished 
him  on  the  chart  must  not  only  possess  an  ac- 
curate background  but  it  must  also  be  presented 
to  the  best  advantage  if  he  is  to  make  the  right 
decision  and  avoid  "guess  work."  The  busy 
executive  is  more  and  more  being  compelled  to 
place  greater  dependence  upon  the  chart  analysis 
of  statistics. 

As  has  been  made  clear,  in  the  practice  of 
chartography  there  is  a  choice  of  widely  varying 
methods.  No  general  rule  can  be  given  for 
determining  which  of  these  methods  is  the  best 
for  any  particular  purpose,  but  practice  will 
enable  one  to  form  his  own  judgment  as  to  selec- 
tion, and  through  experience  he  will  learn  to 


Primary  Principles  of  Chartography  139 

choose  the  method  best  adapted  to  each  of  the 
varying  problems. 

IMPORTANCE     OF    THE     RIGHT    METHOD 

The  importance  of  selecting  the  best  method  is 
emphasized  by  Brinton  in  his  Graphic  Methods 
for  Presenting  Facts.  He  says:  "After  a  person 
has  collected  data  and  studied  a  proposition  with 
great  care  so  that  his  own  mind  is  made  up  as  to 
the  best  solution  for  the  problem,  he  is  apt  to 
feel  that  his  work  is  about  completed.  Usually, 
however,  when  his  own  mind  is  made  up,  his 
task  is  only  half  done.  The  larger  and  more 
difficult  part  of  the  work  is  to  convince  the  minds 
of  others  that  the  proposed  solution  is  the  best 
one — that  all  the  recommendations  are  really 
necessary.  Time  after  time  it  happens  that 
some  ignorant  or  presumptuous  member  of  a 
committee  or  a  board  of  directors  will  upset  the 
carefully  thought  out  plan  of  a  man  who  knows 
the  facts,  simply  because  the  man  with  the  facts 
cannot  present  his  facts  readily  enough  to  over- 
come the  oj)positiori.  It  is  often  with  impotent 
exasperation  that  a  person  having  the  knowledge 
sees  some  fallacious  conclusion  accepted,  or  some 
wrong  policy  adopted,  just  because  known  facts 
cannot  be  marshalled  and  presented  in  such  a 
manner  as  to  be  effective. 


140        Chartogbaphy  in  Ten  Lessons 

"Millions  of  dollars  yearly  are  spent  in  t^i^ 
collection   of   data,   with   the   fond   expectatioif. 
that  the  data  will  automatically  cause  the  cor  ra- 
tion of  the  conditions  studied.     Though  ar  ■ 
data  and  real  facts  are  valuable,  when  it  ■ 
getting  results   the   manner   of  present 
ordinarily  more  importarr*  tian  the  factb  . 
selves.     The  foundation  of  an  edifice  is  of  rnsi 
importance.     Still,  it  is  not  the  foundation  but 
the  structure  built  upon  the  foundation  wh•c^ 
gives  the  result  for  which  the  whole  work  ■v\as. 
planned.     As  the  cathedral  is  to  its  foundation  so 
is  an  effective  presentation  of  facts  to  the  data." 

ESSENTIALS    OF    GOOD    CHART-MAKING 

The  primary  essentials  of  good  chart-making 
are  simplicity  and  clearness.  The  curves  or  bars 
of  a  chart  are  employed  to  express  and  to  com- 
municate ideas,  just  as  words  are  used  in  the 
English  language.  The  fewer  the  ideas  it  is 
attempted  to  express  in  a  single  chart,  the  better. 
In  fact,  a  single  chart  should  aim  to  express  only 
a  single  idea.  This  is  difficult  to  accomplish, 
as  the  essence  of  a  chart  is  a  relation  or  a  compari- 
son and  this  usually  involves  more  than  one  idea. 
The  aim,  however,  should  be  to  construct  the 
chart  so  that  all  but  the  dominant  idea  it  is 
intended    to   express    or    communicate    is    kiept 


Primary  Principles  of  Chartography  141 

subordinate  or  in  the  background.  There  should 
not  be  a  single  unnecessary  mark  or  figure  or 
word  on  the  completed  chart,  and  if  its  full 
meaning  cannot  be  grasped  quickly,  then  it  has 
failed  of  its  object. 

There  is  a  common  and  quite  general  violation 
of  *hese  principles.  Chart-making  is  not  at  all 
complex;  it  does  not  involve  a  knowledge  of 
nigher  mathematics  for  correct  presentation  and 
interpretation.  There  are  a  few  definite  rules 
which,  if  once  understood,  result  in  the  ease  and 
facility  that  may  be  likened  to  a  knowledge  of 
the  alphabet,  once  acquired.  Much  of  bad  chart- 
making  and  of  confu.sion  in  interpretation  flows 
from  a  violation  of  the  few  simple  principles. 

PLANNING    THE   SIZE    OF   THE   CHART 

One  task  that  will  likely  confront  the  student 
with  as  many  jjcrjilexities  as  any  other  will  be 
the  working  out  of  the  size  of  the  chart  within 
the  limitations  of  the  sheet  and  the  requirements 
of  the  statistics.  Only  practice  will  enable  him  in 
time  to  overcome  most  of  these  difliculties.  But 
as  a  .sort  of  guide  for  meeting  .some  of  these  prob- 
lems there  is  [)resent('d  in  the  following  paragraph 
a   practical    illustration. 

The  size  of  the  .sheet  for  the  completed  chart  is 
arbitrarily  fixed  for  u.s  at  12  by   Hi  iiuhcs.     At 


142        Chartography  in  Ten  Lessons 

least  two  of  the  16  inches  are  required  as  a  margin 
on   the  left  of  the  sheet    (the  chart  appearing 
lengthwise)  for  binding.    Usually  an  inch  margin 
on  the  remaining  three  edges  is  advisable.    This 
leaves  13  of  the  original  16  and  10  of  the  original 
12  inches  as  the  size  within  which  the  chartog- 
rapher  is  to  work,  or  a  size  10  by  13  inches.     The 
neat  lines  of  the  frame  and  the  letters  of  the  title 
must  come  within  this  size.  Usually  one-half  inch 
is  sufficient  for  the  title  letters,  and  in  our  particu- 
lar illustration  it  is  required  that  the  title  appear 
lengthwise  of  the  sheet.    This  reduces  the  size  to 
9.5  by  13  inches.    Between  each  of  the  neat  lines 
and  each  of  the  scale  lines    one-half    inch    will 
usually  be  sufficient — this  is  a  reduction  in  both 
dimensions  of  another  inch.     Sometimes  a  full 
inch  is  required  below  the  lower  horizontal  line 
for  the  footnotes.     Of  course  these  spacings  are 
subject  to  being  increased  or  decreased  according 
to  the  requirements  of  varying  problems.     The 
original  size  of  12  by  16  inches  has  dwindled  by  the 
above  mentioned  processes  to  8.5  by  12  inches  as 
the  size  of  the  framework  proper. 

The  arbitrary  limitations  of  space  within  which 
the  chartographer  is  confined  in  his  work  cannot 
be  removed  from  among  the  difficulties  of  the 
practice  of  the  art.  All  that  he  can  do  is  to  learn 
by  experience  to  make  the  best  adjustment  pos- 


Primary  Principles  of  Chartography  143 

sible  in  each  particular  problem.  This  is  true 
no  matter  what  the  size  is  that  is  determined  upon. 
And  having  made  the  decision  the  chartographer 
will  soon  learn  to  adapt  himself  to  the  limitations 
of  space  and  to  forego  something  that  is  desirable 
in  order  to  adjust  his  work  to  the  exigencies  of  the 
requirements. 

In  most  cases  where  a  number  and  variety  of 
charts  are  to  be  filed  for  reference  or  bound  as 
exhibits  it  is  quite  important  that  the  size  for  all 
the  sheets  be  made  uniform.  This  does  not  neces- 
sarily mean  that  the  worker  will  have  the  same 
size  for  the  original  of  all  the  charts  themselves, 
but  it  does  mean  that  the  completed  charts  shall 
all  be  on  sheets  of  the  same  size.  This  permits  of 
uniformity  in  size  for  all  completed  charts  and 
assists  in  securing  neatness  and  orderliness  in 
office  records.  Completed  charts  on  sheets  of 
different  sizes  are  awkward  in  handling  and  easily 
damaged. 

PLANNING   A    REDUCTION   IN   SIZE 

Where  the  original  drawing  is  to  be  reproduced 
by  one  of  the  several  i)hotograj)liic  i)r()oesses  and 
printed  from  j^latcs,  the  chartographer  has  a 
special  problem  of  reduction  in  size  to  solve.  In 
such  cases  tlu*  [)en-aiid-ink  eharf  should  always  be 
considerably  larger  than  the  final  reproduction. 
Most  charts  will  stand  a  reduction  in  size  of  from 


144  CirARTOGKAPHY   IN   TeN   LeSSONS 

one-third  to  one-half  and  in  cases  even  more,  and 
will  be  improved  in  appearance  by  the  process. 
A  reduction  in  the  size  of  the  original  drawing 
tends  to  smooth  out  the  rough  places  or  minor 
irregularities  of  lines,  curves,  bars,  figures,  and 
letters  and  results  in  a  much  cleaner  effect. 
Virtually  all  the  charts  in  these  lessons  have  been 
reduced  approximately  one-half  from  the  size  of 
their  original  drawings. 

In  ascertaining  the  dimensions  for  the  size 
of  the  original  drawing  simply  apply  the  rules  of 
proportion.  Only  four  factors  are  involved — 
the  width  and  length  of  the  reproduced  chart 
and  the  width  and  length  of  the  size  that 
must  be  drawn  to  secure  the  reproduced  size. 
Assuming  our  problem  to  be  the  one  mentioned 
on  page  142,  we  know  the  width  and  length  of 
the  reproduced  size — the  former  is  10  inches  and 
the  latter  13  inches.  We  know  also  how  much  of  a 
reduction  we  desire  to  secure — whether  one- 
third  or  one-half  and  so  on.  Selecting  a  reduction 
of  one-third  gives  us  the  arbitrary  width  of  the 
original  as  15  inches.  It  is  the  length  of  the 
original  that  must  next  be  learned. 

Our  known  figures  give  us  this  formula: 
10  :  13  ::  15  :  X,  which  reads  10  is  to  13  as  is  15  to  x. 
Working  out  this  formula  we  learn  that  13  times 
15  equals  195  and  this  number  divided  by  10  gives 


Primary  Principles  of  Chartography  145 

19.5.  This  latter  thus  represents  our  unknown 
fourth  quantity,  which  is  the  dimension  of  the 
length  of  the  original  drawing.  The  size  of  the 
original  must  then  be  15  by  19.5  inches  to  secure  a 
reduced  size  of  10  by  13  inches. 

In  the  above  illustration  the  number  10  and  the 
letter  x  are  known  as  extremes  and  the  numbers  13 
and  15  as  means.  In  any  proportion  the  product 
of  the  extremes  is  equal  to  the  product  of  the 
means,  that  is,  10  times  x,  the  latter  being  19.5, 
is  195,  the  product  of  the  extremes,  and  13  times 
15  is  195,  the  product  of  the  means. 

It  is  also  true  that  the  product  of  the  extremes 
divided  by  either  mean  gives  the  other  mean,  as 
for  instance:  The  product  of  the  extremes  is  195 
(10  times  19.5)  and  195  divided  by  13,  one  of 
the  means,  gives  15,  the  other  mean, or  195  divided 
by  15  gives  13.  Again,  the  product  of  the  means 
divided  by  either  extreme  gives  the  other  extreme. 
For  illustration:  13  times  15  is  105,  tlie  product  of 
the  means,  and  divided  by  10  gives  19.5,  or  by 
19.5  gives  10. 

Another  siniy)lp  mothorl  for  ascertaining  the 
reduced  dimensions  from  the  original  is  illustrated 
on  the  following  page.  The  larger  rectangle  is 
our  original  si/e.  From  its  lower  Irft  hand  corner 
a  diagonal  line  is  drawn  in  hght  lead  jjcncil  to  the 
upper  right-hand  rf)rn<T.     This  is  line  C-C.    This 


Primary  Principles  of  Chartography  147 

diagonal  line  is  then  connected  by  a  vertical  line 
starting  at  any  point  on  the  base  line  A-A,  such  as 
the  broken  line  shown.  From  the  junction  point  of 
the  broken  line  and  the  diagonal  line  draw  another 
broken  line  at  right  angles  to  the  vertical  line  and 
extending  to  line  D-D.  The  rectangle  thus  cir- 
cumscribed in  the  lower  left  hand  corner  will  be 
found  to  be  in  exact  proportion  to  the  larger  rec- 
tangle, or  the  size  of  the  original. 

In  planning  a  reduction  in  the  size  of  the 
chart  from  the  original,  care  should  be  exercised 
in  .seeing  that  all  the  lines  on  the  original  are  made 
sufficiently  wide  to  stand  the  reduction  in  line 
width  due  to  the  decrease  in  size.  In  our  preced- 
ing illustration  on  page  144  the  lines  would  be  only 
one-third  as  wide  in  the  completed  as  in  the 
original  drawing.  Therefore,  all  the  lines  and 
curves  and  so  on  of  the  origituil  must  be  made 
wider  than  would  be  necessary  if  the  chart  were 
not  to  be  reduced.  Failure  to  allow  for  this  reduc- 
tion in  the  width  of  the  lines  and  curves  and  let- 
ters and  figures  is  a  common  mistake  made  by  the 
beginner  in  chartography  which  should  be 
guarded  against  if  the  best  results  are  to  be 
secured. 

TMK    HP:DrrrNO    cilakh 

A  valnahic  aid  in  this  branch  of  the  work  is  the 
reducing  glass.     It  may  be  .said  to  be  the  opposite 


148        Chartography  in  Ten  Lessons 

of  the  magnifying  glass,  decreasing  instead  of 
increasing  the  size  of  the  object  observed,  the 
lens  being  ground  concave  instead  of  convex. 
A  convenient  size  is  one  with  a  single  lens  about 
one  and  three-fourths  inches  in  diameter.  This 
permits  the  lines,  figures,  and  letters  on  a  chart 
to  be  seen  in  sizes  from  one-half  to  one-fourth 
smaller  than  their  originals. 

In  observing  the  parts  of  the  chart  for  an  in- 
dication of  the  size  of  the  proposed  reduction  the 
most  accurate  method  is  to  hold  the  glass  at 
different  distances  above  the  sheet  so  that  looking 
through  it  with  the  left  eye  two  or  three  or  four 
squares,  depending  upon  the  amount  of  reduction 
desired,  equals  one  square  as  seen  by  the  unob- 
structed right  eye.  Thus  by  superimposing  and 
comparing  the  images  of  both  eyes  the  required 
reduction  can  be  measured.  This  enables  a 
comparison  of  the  width  of  lines,  figures,  and 
letters  as  originally  placed  with  their  width  after 
reduction  and  permits  the  determination  as  to 
whether  they  must  be  made  still  wider  or  heavier 
or  larger  in  order  to  meet  the  reduced  size. 
Even  with  the  use  of  the  reducing  glass  the  be- 
ginner is  likely  to  find  at  first  that  his  lines, 
curves,  figures,  letters,  and  so  on  when  reproduced 
do  not  appear  to  be  as  heavy  or  as  large  as  he  had 
anticipated. 


Primary  Principles  of  Chartography  149 

Without  the  emploj'ment  of  these  rules  and 
aids  in  reduction  one  has  to  depend  largely  upon 
guess  work  as  to  whether  the  chart  and  its  parts 
will  present  a  proper  appearance  when  reduced, 
and  guess  work,  as  has  been  said,  should  be 
eliminated  from  chartography.  The  student 
must  not  forget  that  accuracy  is  a  valuable 
mental  quality  which  is  useful  elsewhere  than  in 
chartography,  and  if  the  practice  of  this  art 
teaches  it  to  him  he  has  gained  an  additional 
asset  of  great  usefulness, 

TUE  FRENCH  CURVES 

Another  tool  that  the  student  may  find  useful, 
especially  in  cliarting  curves,  is  what  is  known  as 
the  "French  curves."  These  are  on  sale  at  any 
first-class  store  dealing  in  drafting  instruments. 
While  they  do  not  always  in  their  entirety  fit  into 
the  complete  curve  the  student  has  to  make,  they 
can  be  shifted  forward  or  bafkward  so  as  to  cover 
fairly  accurately  the  lead-pencil  dots  measuring 
the  points  of  contact  of  the  curve.  Usually 
they  give  a  clean,  smooth  curve  if  care  is  exercised 
in  their  use. 

In  most  charts  where  the  scale  units  perniil  flic 
curve  to  move  regularly  up  or  down  across  the 
sheet,  the  curve  appears  smooth  without  sharp 
movements    that    result    in    peaks.     In    all    the 


150        Chartography  in  Ten  Lessons 

illustrations  in  these  Lessons  these  curves  have 
been  drawn  in  freehand,  and  this  method  is 
recommended  as  satisfactory.  This  peak-top 
does  not  indicate  as  minute  a  degree  of  accuracy 
in  the  figures  upon  which  the  curve  is  based  as 
does  the  smooth  curve. 

OTHER  MECHANICAL  AIDS 

One  serious  drawback  in  making  the  letters  by 
hand  is  the  length  of  time  required,  even  after  one 
becomes  proficient  in  lettering.  Under  conditions 
where  the  number  of  charts  to  be  drawn  is  large, 
efficiency  is  best  served  and  the  cost  of  produc- 
tion materially  reduced  if  recourse  is  had  to  a 
small  printing  press  with  about  three  fonts  of 
type  of  18,  12,  and  10  point,  commercial  Gothic. 
The  moderate  expenditure  will  soon  be  com- 
pensated by  using  for  other  work  the  time  saved 
from  lettering  by  hand.  Printed  letters  photo- 
graph satisfactorily  in  almost  any  process  of 
reproduction. 

Another  recourse  instead  of  drawing  letters  by 
hand  is  to  make  use  of  gummed  black  paper 
letters  and  figures  which  are  for  sale  at  first- 
class  stationery  stores.  These  can  usually  be 
pasted  quite  neatly  on  the  chart  that  is  to  be 
reproduced,  if  a  light  pencil  line  is  made  for  a 
guide  along  the  bottom  of  the  spacing  for  the 


Primary  Principles  of  Chartography  151 

letters.     This  pencil  line  must  of  course  afterwards 
be  erased. 

CHECKING-UP  THE  COMPLETED  CHART 

After  the  drawing  has  been  finished  there 
remains  for  the  student  a  very  important  task. 
The  explanation  of  this  task  in  detail  involves 
describing  the  concrete  application  of  all  the 
rules  and  principles  of  chartography  that  have 
been  observed  in  the  construction  of  the  chart. 
This  is  true  in  the  sense  that  the  student  must  see 
to  it,  by  a  rigid  and  thorough  checking-up  of  the 
lines  and  figures  and  letters  and  so  on  before  the 
chart  leaves  his  hands,  that  all  these  rules  have 
been  strictly  applied.  As  related  to  the  check- 
ing up  of  certain  features  of  the  curve  chart, 
this  task  has  already  been  referred  to  in  I^esson 
IV',  pages  50  and  51.  The  immediately  follow- 
ing statements  apply  particularly  to  the  bar  chart. 

Each  bar  should  extend  to  the  {mint  on  the 
chart  that  its  .statistical  number  as  measured  by 
the  scale  determines — it  should  neither  fall  short 
of  this  point  nor  extend  beyond  it. 

Be  sure  that  each  bar  is  properly  spaced  from 
adjoining  bars. 

In  making  the  f)ars  of  a  chart  it  is  quite  often 
possible  that  all  the  space  to  the  right  of  the 
vertical  scale  or  column  of  years  and  to  the  left  of 


152        Chartography  in  Ten  Lessons 

the  ends  of  the  bars,  and  from  the  horizontal 
scale  line  to  the  base  line,  can  be  made  black 
with  a  small  brush  dipped  in  India  ink,  the  ends 
of  the  bars  being  squared  with  the  pen.  After 
the  ink  dries  the  bars  can  easily  be  outlined  and 
separated  from  each  other  according  to  the  ver- 
tical scale  units  by  drawing  horizontal  lines  in 
Chinese  white.  This  expedient  enables  a  great 
deal  of  work  to  be  done  in  a  comparatively  short 
space  of  time,  and  the  results  are  highly  satis- 
factory. When  the  India  ink  is  used  in  this  way 
it  is  advisable  to  apply  two  or  more  coats  or 
washes  in  order  to  insure  a  uniform  density  of 
surface. 

Chinese  white  is  an  opaque  composition  which 
may  be  thinned  down  to  desired  consistency  by  the 
addition  of  water.  Besides  its  use  in  separating 
bars  out  of  a  block  of  black,  Chinese  white  is  also 
excellent  for  concealing  black  ink  lines  or  marks 
where  erasure  is  impracticable. 

The  scale  units  should  be  correct  at  each  of  the 
points  of  measurement  and  neither  to  the  right  nor 
left  of  their  proper  places. 

The  chart  should  include  the  statistical  table 
from  which  it  has  been  made. 

If  it  is  found  impossible  to  include  the  statistical 
table  on  the  chart  it  should  be  on  an  accompany- 
ing or  attached  slip  or  sheet. 


Primary  Principles  of  Chartography  153 

The  table  of  figures  should  be  correct  and  neat 
and  properly  located  and  boxed  without  crowding. 

The  period  of  time  column  both  in  the  table 
and  adjacent  to  the  bars  must  be  correctly  and 
properly  alligned. 

Be  sure  that  no  mistake  has  been  made  in  copy- 
ing any  figures  on  to  the  chart. 

The  statistical  table  involving  periods  of  time 
should  be  presented  with  the  earliest  period  first. 

The  source  of  the  statistical  table  should  in 
every  instance  be  given,  preferably  in  the  foot- 
notes. 

Instead  of  checking  up  the  movement  of  the 
bars  or  curves  from  either  the  statistical  table  on 
the  chart  or  tlie  scale  figures  themselves,  reference 
should  be  had  to  the  original  figures. 

All  additions,  subtractions,  multiplications, 
divisions,  and  so  on  derived  from  the  statistical 
table  should  l)e  computed  at  least  twice  and  by 
different  persons. 

See  that  all  horizontal  lettering  reads  from  left 
to  right  and  all  vorticul  lettering  from  the  base 
of  the  chart  uj>ward. 

The  title  should  be  clear  and  concise  and  yet 
comprehensive.  It  shoiilci  have  every  word 
spelled  correctly  and  should  contain  the  fewest 
possible  words  consistent  with  clearness  of  ex- 
pression.    It  sometimes  happens  that  the  title 


154        Chartography  in  Ten  Lessons 

can  be  improved  in  these  directions  over  the  first 
selection  of  words  after  the  student  has  been 
working  with  the  statistical  material.  Words  as 
well  as  letters  in  the  title  should  be  evenly  placed 
and  spaced — none  of  them  must  be  askew. 

THE  PROCEDURE  IN  CHECKING  UP 

It  is  an  advantage  in  checking  up  a  chart  to 
start  with  the  title,  next  the  horizontal  scale,  then 
the  vertical  scale,  the  table  of  statistics,  and  then 
relate  the  movement  of  the  curves  or  bars  to 
these  factors.  The  horizontal  and  vertical  lines 
forming  the  background  of  the  chart  must  not  be 
overlooked  as  to  their  proper  distance  apart. 
The  foot-notes  and  the  neat  lines  require  equally 
careful  attention. 

Make  sure  that  the  neat  lines  are  wider  or 
heavier  than  the  vertical  and  horizontal  lines  of 
the  framework. 

Foot-notes  should  be  as  brief  as  possible  con- 
sistent with  clearness,  should  read  from  left  to 
right,  and  should  not  be  askew. 

In  selecting  the  designations  for  the  curves  and 
bars,  have  the  most  conspicuous  been  made  to 
correspond  with  the  particular  statistical  element 
it  is  desired  to  emphasize?  For  instance,  in  bar 
designations  the  solid  black  is  generally  more 
noticeable. 


Primary  Prinxiples  of  Chartography  155 

Check  carefully  the  key  or  legend  designations 
with  those  of  the  curves  and  bars  to  see  that 
they  correspond  accurately. 

Have  the  proportions  been  correctly  determined 
for  the  required  reduction? 

Be  especially  careful  that  all  lead  pencil  and 
unnecessary  ink  marks,  used  as  guides  or  other- 
wise, have  been  erased  or  removed.  If  not,  in 
case  of  reproduction  these  are  likely  to  photograph 
and  thus  affect  disadvantageously  the  neat  ap- 
pearance of  the  chart. 

CLEANLINESS  ESSENTIAL  TO  NEATNESS 

In  handhng  a  chart  keej)  the  hands  clean, 
especially  from  the  drawing  ink  which  will  smear 
the  sheet.  .\n  aid  to  this  will  be  found  by  keeping 
the  ink  bottle  on  a  blotter  which  will  absorb  drops 
and  i)rovent  them  from  getting  on  the  drawing 
board  or  table.     Blot  immediately  every  ink  spot. 

Never  fold  a  rliart.  Keep  the  sheet  flat  or 
roll  it.  A  foldeil  chart  cracks  or  creases  the  .sheet 
and  breaks  the  lines,  bars,  curves,  and  .so  on. 

All  checking  arul  verification  sjioiild  l)e  done 
also  by  somr  f)nc  other  tliaii  the  person  who  drew 
the  chart  .so  that  there  may  be  greater  certainty  in 
the  detection  and  eorreetiori  of  errors.  For 
even  the  Invst  chartographer  makes  mistakes. 

The  student  should  assure  himself  before  per- 


156        Chartography  in  Ten  Lessons 

mitting  the  chart  to  leave  his  hands  as  completed 
that  in  all  respects  it  is  in  condition  to  receive  his 
final  O.  K. 

PLOTTING  THE  CHART  IN  ROUGH  OUTLINE 

After  the  chartographer  has  completed  his 
checking  up  he  should  devote  several  minutes  to  a 
consideration  of  the  possibility  that  he  might 
have  selected  a  different  method  which  would 
have  brought  out  the  point  of  the  statistics  more 
clearly.  He  will  have  fewer  regrets  if  he  adopts 
and  consistently  follows  the  practice  of  first 
plotting  his  chart  in  rough  outline  in  lead  pencil 
at  the  very  outset  of  his  work.  He  should  apply 
this  to  several  methods  before  finally  determining 
upon  any.  He  will  find  that  though  this  practice 
takes  a  little  time  at  first  it  will  in  the  end  greatly 
expedite  his  work. 

It  should  never  be  forgotten  that  as  chartog- 
raphy primarily  supplements  statistics  with  the 
object  of  making  them  clear  and  comprehensible 
at  a  glance,  a  chart  that  is  not  more  clear  in 
exposition  than  the  statistical  data  upon  which 
it  is  based  has  missed  its  object.  Also  it  should 
be  remembered  that  the  chart "  tells  the  story  " — 
it  should  need  very  little  explanation,  if  any. 

Instructions  to  the  lithographer  should  be  clear 
and  definite.    These  may  be  written  on  a  slip  of 


Primary  Principles  of  Chartography  157 

paper  and  attached  to  the  drawing  with  a  clip, 
but  a  safer  plan  is  to  write  them  on  the  coordinate 
sheet  itself,  preferably  on  the  back. 

Before  sending  the  drawing  to  be  reproduced 
be  sure  to  cut  away  the  margin  of  the  sheet  where 
the  thumb  tacks  have  held  it  in  place  on  the 
drawing  board,  as  these  punctures  are  likely  to 
show  in  the  reproduced  chart.  Even  when  the 
drawing  is  not  to  be  photographed,  such  punc- 
tures in  the  paper  detract  from  the  neat  ap- 
pearance of  the  finished  chart. 

Before  deciding  upon  the  uniform  size  of  sheet 
for  a  number  of  different  kinds  of  charts  it  is 
advisable  to  consult  the  lithographer  in  order  that 
a  size  may  be  selected  which  i)erniits  of  the  least 
possible  waste  orloss  in  cuttingfrom  the  larger  sheet. 

It  is  imf)()rtaiit  also  to  examine  closely  into 
the  quality  of  the  {>ai)er  of  the  reproduced  chart. 
The  preservation  of  the  chart  depends  to  a  large 
degree  upon  this  quality.  Paper  containing 
sulphite  i)ulp  or  other  chemicals  suffers  rapid 
deterioration.  Within  a  .short  time  such  paper 
becomes  l)rittlp  and  discolored,  and  these  defects 
seriously  affect  the  preservatir)ti  of  chart  records 
for  any  length  of  time.  \  high  grade  linen  bond 
paper,  althongh  it  co.sts  more  per  sheet,  is  less 
expensive  in  the  long  nm. 

The  checking  up  of  the  com|>letetl  chart  as  well 


158       Chartography  in  Ten  Lessons 

as  the  details  of  the  planning  and  drawing  should 
impress  upon  the  student  the  necessity  for  observ- 
ing closely  and  carefully  every  factor  with  which 
he  deals.  He  cannot  afford  to  overlook  even 
the  smallest  detail  as  every  detail  must  be  accurate 
if  the  completed  chart  is  to  be  accurate.  This 
attention  to  minor  details  fixes  the  mind  upon 
the  correctness  of  the  figures;  on  the  accuracy 
of  the  scale  units;  on  the  spacing  of  figures  and 
lines;  on  the  spelling  of  words;  on  the  correct 
designation  and  spacing  and  length  of  the  bars, 
and  so  on.  Looking  for  possible  defects  or 
errors  develops  the  critical  faculties.  In  the 
course  of  practice  all  these  separate  but  important 
details  soon  fix  a  habit  of  mind  and  that  which  at 
first  may  be  hard  work  sooner  or  later  becomes 
almost  mechanical  attention.  Working  with 
tools  that  require  accuracy  in  their  use  the 
chartographer  soon  learns  from  mistakes  he  must 
correct  that  it  does  not  pay  to  make  mistakes — 
that  it  is  a  loss  of  time  and  energy  and  materials 
— and  he  comes  consciously  to  apply  himself  so 
as  to  avoid  their  repetition  in  order  not  to  be 
compelled  to  do  the  work  over  again.  Out  of  this 
experience  he  learns  efficiency  in  the  concen- 
tration of  his  energies  and  in  their  application  to 
his  specific  task.  Chartography  is  thus  an 
invaluable  mental  training.     It  lends  accuracy  to 


Primary  Principles  of  Chartography  159 

constructive  thinking;  it  leads  to  the  further  study 
,  of  statistics  and  of  the  underlying  forces  back  of 
them,  and  by  these  and  similar  steps  the  pro- 
gressive student  develops  his  thinking  capabilities. 

QUESTIONS  FOR  SELF-EXAMINATION 

1.  What  is  meant  by  planning  the  chart?    How  does  it 
differ  from  plotting  the  chart? 

2.  Discuss  the  importance  of  selecting  the  right  method. 

3.  What  are  the  essentials  of  good  chartography? 

4.  How  is  the  size  of  the  chart  planned? 

5    How  is  a  reduction  in  size  of  the  original  determined? 

6.  Of  what  assistance  is  the  reducing  glass? 

7.  What  are  "French  curves"? 

8.  Describe  the  more  important  phases  of  checking  up 
the  completed  chart. 

9.  Summarize  briefly  the  more  important  of  the  funda- 
mental principles  of  chartography. 

10.  Of  what  value  is  chartography  in  training  the  mind? 


This  book  is  DUE  on  the  Itist  date  stamped  below 


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